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# rgbstudios / replacement-calc

Use Replacement Calc to calculate the probabilities of picking a certain number of objects without replacement, such as picking marbles or cards

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Commit time # Picking Without Replacement Probability Calculator - RGB Studios

### Use Replacement Calc to calculate the probabilities of picking a certain number of objects without replacement, such as picking marbles or cards

rgbstudios.org/replacement-calc

### Parameters

Enter the following inputs:

• Total number of items (N)

• Number of distinct items (m)

• Number of items picked (n)

• Number of distinct items picked (k)

Then:

• Click "Calculate" and view the probability of exactly k distinct items picked, as well as the cumulative probability of less or more successes

• View the odds of less, than, equal to, or greater than k distinct items picked as a pie chart and bar graph

• Exactly that many is in blue, less than is in red, greater is in green

### Uses

• Studying statistics

• Drew too many or too few lands or energy in a tcg

• Playing games with a standard 52 or 54 card poker deck

### Formulas:

When picking n items out of N total items, where m of them are distinct, the odds of picking exactly k distinct items is defined as:

• P(X = k) = mCk * N-mCn-k / NCn

Where nCx ("n choose x") is defined as

• nCx = n! / [ x! (n - x)! ]

V.1.0.1

by Justin Golden for RGB Studios

justingolden21.github.io

Use Replacement Calc to calculate the probabilities of picking a certain number of objects without replacement, such as picking marbles or cards