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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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File `mychemistry.sty' not found.
Emergency stop.
leading text: \usepackage

r=3

Step 2: Find combination that you are part of

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

r=2

Step 3: Calculate Probability

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