In 9 Choose 3: What Are the Odds of Choosing the Same Value Twice?
Discover the probabilities and chances of selecting the same value twice in a 9 choose 3 scenario. Explore the fascinating world of combinations and permutations to understand the likelihood of such an occurrence.
Have you ever wondered what the odds are of selecting the same value twice in a scenario where you choose 3 out of 9 options? In this article, we will delve into the world of combinatorics and probability to determine the likelihood of such an event.
Understanding Combinations and Permutations
Before we dive into the odds, let's quickly review the concepts of combinations and permutations. In combinatorics, combinations refer to the selection of items from a larger set without considering the order in which they are chosen. On the other hand, permutations involve the arrangement of items in a specific order.
In the case of "9 choose 3," we are interested in finding all possible combinations of 3 values selected from a set of 9 options, without repetition. This means that once a value is chosen, it cannot be chosen again.
Calculating the Number of Combinations
To calculate the number of combinations in "9 choose 3," we can use the
What is the triple birthday paradox?
Is birthday paradox true?
What is the probability that at least two people out of the 9 share a birthday?
What are the odds of 3 random people having the same birthday?
What is the rarest birthday?
December 25 (Christmas Day) is the least common birthday, while January 1 (New Year's Day) is the second least common. December 24 (Christmas Eve) also makes the list as the 3rd least common birthday while July 4 (Independence Day) is the 4th least common birthday.
How do you calculate odds?
Frequently Asked Questions
What is the probability of four of a kind?
5card poker hands
Hand  Distinct hands  Probability 

Four of a kind  156  0.02401% 
Full house  156  0.1441% 
Flush (excluding royal flush and straight flush)  1,277  0.1965% 
Straight (excluding royal flush and straight flush)  10  0.3925% 
How many possible combinations of 6 items are there?
How many ways can 3 items be selected from a group of 6 items?
3 items need to be selected put of 6. So selection ways will be 6C3 = 20.
How many ways can 6 numbers be arranged?
How do you calculate combined probability?
How do you calculate odds together?
How do I calculate the number of possible combinations?
How do you calculate the odds of a 4 digit combination?
What is the formula for combination odds?
How do you calculate possible combinations of two numbers?
How do you find the probability of a combination?
 Permutation with repetition: Total permutations = n^r.
 Permutation without repetition: Total permutations for a selection = n! / (n  r)!
 Combination with repetition: Total combinations = n! / (r!
 Combination without repetition: Total combinations = (r + n  1)! / (r!
How many possible combinations are there for a 2 digit number?
How many combinations if you pick 2 out of 4?
represents the factorial function (e.g., 4! = 4 x 3 x 2 x 1). Therefore, there are 6 combinations of 4 objects taken two at a time.
How do you find probability with three variables?
 P ( A ) , P ( B ) & P ( C )
 P ( A ∩ B ∩ C ) = P ( A ) × P ( B ) × P ( C ) .
 Hence, the probability of three independent events is P ( A ∩ B ∩ C ) = P ( A ) × P ( B ) × P ( C ) .
How do you calculate statistical odds?
What are the odds of picking 3 numbers?
FAQ
 What are the odds of getting a pair in 3 cards?
 Three Card Poker: What to Expect.
 Queen High or better: 69.59%
 Pair: 16.94%
 Flush: 4.96%
 Straight: 3.26%
 Three Of A Kind: 0.24%
 Straight Flush: 0.22%
 How do you calculate the odds of multiple events?
 Multiplication Rule (Dependent Events)
P(A and B) = P(A) * P(B  A), where P(B  A) is the probability of event B given that event A happened. When P(B  A) is the probability of event B given that event A happened.
 What is the probability of 5 9?
 In this case, we have 5 wins, and 9 losses, which is a total of 14 times “playing” the contest. So we win 5 out of 14 total, or about 35.71% of the time.
 What are the odds of winning the 5 number lottery?
 Step 1: The chance of getting 5 numbers correct out of 5 numbers drawn from 69 unique numbers is 1 in 11,238,513 (see #1, Step 1 above.) Step 2: The chance of correctly choosing the Powerball is 1 in 26.
 What is the probability of getting 5 numbers in a row?
 On all draws, you have a 1/5 chance, so the P(5,5,5,5,5)=1/5*1/5*1/5*1/5*1/5, or 1/5^5. This comes out to 1/3125, or approximately 0.00032. A number is selected at random from the numbers 3, 5, 5, 7, 7, 7, 9, 9, 9, 9.
 What are the odds of choosing the same number?
 The answer is 1/100. If both people pick a number, the number that person 1(or person 2, it doesn't matter) chooses does not matter. When that number is selected, person 2 has a 1/100 chance of picking the same number, no matter what number person 1 picked.
 How many ways can you choose 5 from 9?
 The number of ways of choosing 5 items out of a set of 9 = 9 C 5 (pronounced “9 choose 5”) = 9!/(5! x 4!) = (6 x 7 x 8 x 9)/(1 x 2 x 3 x 4) = 3,024/24 = 126.
 What is the formula for calculating odds?
 To convert from a probability to odds, divide the probability by one minus that probability. So if the probability is 10% or 0.10 , then the odds are 0.1/0.9 or '1 to 9' or 0.111. To convert from odds to a probability, divide the odds by one plus the odds.
 How do you calculate the probability of an outcome?
 What is the formula for calculating probability? To calculate probability, you must divide the number of favorable events by the total number of possible events. This generates a sample, and the calculation can be performed from the data obtained.
 How do you calculate percentage of outcomes?
 To calculate a percentage, follow these steps:
 Determine the number of items in the subgroup of interest for the numerator.
 Determine the total group size for the denominator.
 Divide the numerator by the denominator.
 Multiply the decimal by 100 to find the percentage.
 How do you calculate the odds of something happening?
 To calculate probability, you'll use simple multiplication and division. Probability equals the number of favorable outcomes divided by the total number of outcomes.
 How do you find the odds of multiple events?
 To determine the probability of two independent events, and , both occurring, we multiply the probabilities of each of the two events together: P ( A ) × P ( B ) = P ( A a n d B ) .
 How many combinations of 4 with 10 numbers?
 5040
We could either compute 10 · 9 · 8 · 7, or notice that this is the same as the permutation 10P4 = 5040.
 What are the odds of matching a 4 digit number?
 One in 10,000
It's very simple. In 4 decimal digits there are 10,000 (0000 to 9999) possible values. The odds of any one of them coming up randomly is one in 10,000. A specific "4 digit number" would have 1/9000 chance, since there are 9000 4 digit numbers (10009999).
 What is the probability of guessing a 4 digit PIN code out of 10 numbers?
 1,000 X 10 = 10,000 choices if digits can repeat. If digits can not repeat the first digit would have 10 choices, second 9, third 8, and fourth 7. 5,040/10,000 = 0.504 = 50.4% chance of having 4 digit pin without repeating digits.
 How many combinations of 4 options are there?
 24 combinations
Given that there are 4 possibilities for the first, then 3, 2, 1 respectively, the formula is n! If you are asking how many unique combinations/sequencies you can make out fd the 4 letters, it is 4! There would be 24 combinations using 4!
If you have 6 options and you need to pick the correct pair what are the odds you will get it right
How many permutations of 10 things taken 4 at a time?  Hence, the number of permutations of 10 objects, taken 4 at a time is 5040.  
What are the odds of rolling a 6 with 2 dice?  Eleven times out of 36 or 30.5 %, slightly less than the 33.3% (2/6). When you roll two dice, you have a 30.5 % chance at least one 6 will appear. This figure can also be figured out mathematically, without the use of the graphic.  
What is the probability of getting 1 out of 6?  Number Converter


How do you calculate odds of something happening multiple times?  Multiplication Rule (Dependent Events)
P(A and B) = P(A) * P(B  A), where P(B  A) is the probability of event B given that event A happened. 

What has a 1 4 chance of happening?  An example of a 1 in 4 chance event where successive trials are independent would be: Getting 2 heads when tossing 2 fair coins. Getting a particular outcome on tossing a fair die which has 4 faces (i.e. a tetrahedron).  
What are the odds of rolling a 1 or 5 with 6 dice?  If so, since each die has six numbers there are a total of 36 numbers on six dies. There are six 1s and six 6s on the six dies. The probability of rolling a 1 or a 5 is 12/36 or 1/3.  
What are the odds of matching a 6 digit number?  If all numbers 0–9 are allowed (and no nonnumbers), there are 10^6 possible 6 digit combinations. The odds of guessing the correct one are 1 in a million. 1/10^6 or one in a million if guesses are random or the PIN is selected randomly or both.  
What are the odds of guessing a 6 digit passcode?  A 1/1,000,000 chance
In your example, we can think about it as follows: A sixdigit code has 1,000,000 possible states, hence allows for a 1/1,000,000 chance to correctly guess it on the first try. 

How many probabilities are there in 6 digit numbers?  The probability of a 6 digits number with no repeats is basically the number of permutations of 6 digits with no repetitions among the set of all possible numbers, so the probability is given by P(E)=P(10,6)106=0.1512.  
How many combinations of 6 numbers are there?  But we don't care which order our numbers are picked, and the number of different ways of picking 6 numbers are 6 x 5 x 4 x 3 x 2 x 1 = 6! = 720. Therefore our six numbers are one of 49 x 48 x 47 x 46 x 45 x 44 / 6! = 13983816 so we have about a one in 14 million chance of hitting the jackpot.  
Is it possible to guess a 6 digit code?  Six digit password has 10^6 possible combinations(million possible combination). Normal cracking it with a powerful CPU that tries 30 passwords/second would take 9.25 hours which is quite long.  
What is the probability of 3 and 4?  The number 3 can show up once and 4 can show up once. So, out of six possible outcomes, two of them are really what we are looking for. Therefore, the required probability is 2/6 or 1/3.  
What are the odds 3 people have the same birthday?  The chance of: two people sharing a birthday would be 1  (364/365), or 0.3%, or 1 in 370. three people sharing a birthday would be 1  ((364/365)(363/365)), or 0.8%, or 1 in 122.  
Is the birthday paradox true?  The birthday paradox refers to the counterintuitive fact that only 23 people are needed for that probability to exceed 50%. The birthday paradox is a veridical paradox: it seems wrong at first glance but is, in fact, true.  
What is the formula for probability?  Calculating probabilities is expressed as a percent and follows the formula: Probability = Favorable cases / possible cases x 100.  
What is the probability sum of 3 dice is 4?  1.4%
We divide the total number of ways to obtain each sum by the total number of outcomes in the sample space, or 216. The results are: Probability of a sum of 3: 1/216 = 0.5% Probability of a sum of 4: 3/216 = 1.4% 
 How do you find statistical odds?
 To convert from a probability to odds, divide the probability by one minus that probability. So if the probability is 10% or 0.10 , then the odds are 0.1/0.9 or '1 to 9' or 0.111.
 How do you find the probability of a pair?
 And then 2 3 4 all the way to a king you've got 13 of those and from them you need to choose two of them for your two pair. So here the two are the 7. And the jack.
 How do you calculate combination odds?
 The four combination probability equations are:
 Permutation with repetition: Total permutations = n^r.
 Permutation without repetition: Total permutations for a selection = n! / (n  r)!
 Combination with repetition: Total combinations = n! / (r!
 Combination without repetition: Total combinations = (r + n  1)! / (r!
 The four combination probability equations are:
 What are the odds of drawing a pair?
 Therefore, the overall probability of drawing a pair is the product of the two probabilities, which is 1 * 3/51 = 3/51, or approximately 0.0588, or 5.88%. So, the probability of getting a pair by drawing two cards separately from a 52card deck is approximately 5.88%.
 What are the statistical odds?
 In statistics, odds are an expression of relative probabilities, generally quoted as the odds in favor. The odds (in favor) of an event or a proposition is the ratio of the probability that the event will happen to the probability that the event will not happen.
 What are the odds of matching 5 numbers?
 Step 1: The chance of getting 5 numbers correct out of 5 numbers drawn from 69 unique numbers is 1 in 11,238,513 (see #1, Step 1 above.) Step 2: The chance of correctly choosing the Powerball is 1 in 26.
 What are the odds of guessing a 5 digit number?
 So there are 100,000 total combinations of passwords. Hence, the odds the hacker guesses is 1 out of 100,000 .
 What is the probability of 5 numbers?
 Calculate your odds of choosing correctly.
The result tells you there are 11,238,513 possible combinations of 5 numbers in a set of 69 unique numbers. This means that you have a 1 in 11,238,513 chance of choosing the five numbers correctly.
 Calculate your odds of choosing correctly.
 What is the probability of 1 to 49 combinations of 5?
 1/1906994
The probability of choosing a desired set of 5 numbers from 49 numbers is the total combinations of 5 out of 49. So it is 1/49C5= =5!( 49–5)!/49! =1/1906994.
 1/1906994
 What is the probability of guessing 5 out of 7 numbers?
 I would like to find the probability of guessing 5 out of 7 numbers. There is 34C7 possibles. The correct answer is 0.0014.
 How do you find the odds of two things happening?
 To determine the probability of two independent events, we have to multiply the probability of the first event by the probability of the second event.
 How do you calculate selection odds?
 The formula for calculating odds is:Odds = Probability of event occurring / Probability of event not occurringFor example, if the probability of winning a game is 1/4 (or 0.25), the odds of winning are:Odds of winning = 0.25 / (1  0.25) = 0.25 / 0.75 = 1/3 (or "1 to 2")
 How do you calculate chances of getting something?
 What is the formula for calculating probability? To calculate probability, you must divide the number of favorable events by the total number of possible events. This generates a sample, and the calculation can be performed from the data obtained.
 What are the 4 types of probability?
 What are the types of probability? Probability is the branch of mathematics concerning the occurrence of a random event, and four main types of probability exist: classical, empirical, subjective and axiomatic.
 What is the chance of getting a certain outcome?
 How to Compute Probability. To compute the probability of an event, divide the number possible outcomes by the number of total outcomes. For example, rolling a 3 in a die is 1 possible outcome over 6 possible outcomes, which gives us 1/6.