Combinations Calculator
This calculator determines the number of ways to select
y out of
x items when the order in which they are selected does not matter.
Example  Value for x  Value for y 
Determine the number of possible starting hands in a regular video poker game  52  5 
Permutations Calculator
This calculator determines the number of ways to select
y out of
x items when the order in which they are selected does matter.
Example  Value for x  Value for y 
Determine the number of unique possible B, I, G, or O columns on a Bingo card  15  5 
Determine the number of unique possible N columns on a Bingo card  15  4 
The total number of unique Bingo card permutations is therefore:
Permut(15, 5) × Permut(15, 5) × Permut(15, 4) × Permut(15, 5) × Permut(15, 5) =
552,446,474,061,128,648,601,600,000

Hypergeometric Distribution Calculator
This calculator determines the probability of matching
d out of
c numbers when
b numbers are randomly selected from a pool of
a numbers.
This is useful for determining probabilities in Bingo, Keno and Lottery games.
Example  Value for a  Value for b  Value for c  Value for d 
Determine the odds of matching 4 out of 6 numbers in a traditional keno game  80  20  6  4 
Determine the odds of matching 5 numbers in a lottery where 6 numbers from 1 to 50 are chosen  50  6  6  5 
Determine the odds of having a full bingo card after 50 numbers are called  75  50  24  24 
Practical Applications
Determining the odds of winning the
Powerball can be done by using the Combinations Calculator:
 Calculate the number of ways to select 5 of the 55 regular numbers = 3,478,761 combinations
 Calculate the number of ways to select 1 of the 42 Powerball numbers = 42 combinations
 Multiply the results together: 3,478,761 × 42 = 146,107,962.
There are a total of
146,107,962 ways to select (5 out of 55) and (1 out of 42) numbers. Only one of these combinations will win the jackpot. Therefore, the odds of winning the Powerball
are
1 in 146,107,962.
To calculate the odds of matching 4 regular numbers without matching the Powerball, do the following:
 Using the Hypergeometric Distribution Calculator, calculate the odds of matching 4 of 5 numbers when 5 of 55 are selected = 1 in 13,915.0440
 Using the Combinations Calculator, determine the number of ways to select 41 out of 42 numbers = 42
 Multiply the results together: 13,915.0440 × 42 = 584,431.8480
Therefore, the odds of matching 4 of 5 numbers without the Powerball are about
1 in 584,431.85.