Question

in how many ways can a person select 3 golf shirts for vacation from a selection of 10 golf shirts?

\\{}_{n}c_{r} = \frac{n!}{r!(n-r)!}\\

Explanation:

Identify the parameters

$$ n = 10, \quad r = 3 $$

Apply the combination formula

$$ {}_{10}C_{3} = \frac{10!}{3!(10-3)!} = \frac{10!}{3! \cdot 7!} $$

Simplify and calculate

$$ {}_{10}C_{3} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120 $$

Answer:

120