Use Counting Principle, Combinations, and Permutations to Compute Probability

You are on a chess team made up of 15 players. What is the probability that you will be chosen if a 3-person team is selected at random?

Combinations of n Objects Taken r at a Time:

  • The number of combinations of r objects taken from a group of n distinct objects is denoted by nCr and is given by the formula:
    • nCr = \frac{n!}{(n-1)!r!}


Step 1: Find all combinations

n \pm 15     15C3 =

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\frac{15!}{(15-3)! 3!

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Step 2: Find combination that you are part of

n=14                              14C2 = \frac{14!}{(14-2)!2!}


Step 3: Calculate Probability

\frac{\frac{14!}{12!2!}}{\frac{15!}{12!3!}} =\frac{3}{15} = \frac{1}{5}$