N Choose k
Overview
- represents the number of ways to choose successes from trials without regard to order.
- Binomial Coefficient:
- : Factorial of $ n $, the product of all positive integers up to $ n $.
- : Factorial of $ k $.
- : Factorial of .
Example
- Coin Flipping:
- Suppose we want to find the number of ways to get exactly 3 heads in 5 coin flips.
- Using the binomial coefficient:
- So, there are 10 different ways to get exactly 3 heads in 5 coin flips without regard to order.
