# 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 =

Step 1: Find all combinations

15C3 =

*** QuickLaTeX cannot compile formula:
\frac{15!}{(15-3)! 3!

*** Error message:
Emergency stop.

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r=3

Step 2: Find combination that you are part of

n=14                              14C2 =

r=2

Step 3: Calculate Probability

\frac{3}{15} = \frac{1}{5}\$