Question

in how many ways can a member of a hiring committee select 3 of 12 job applicants for further consideration?

\\_nc_r = \frac{n!}{r!(n-r)!}\\

Explanation:

Identify the parameters

$$
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$$

Apply the combination formula

$$ _{12}C_3 = \frac{12!}{3!(12-3)!} = \frac{12!}{3! \cdot 9!} $$

Simplify and calculate

$$ _{12}C_3 = \frac{12 \times 11 \times 10}{3 \times 2 \times 1} = 220 $$

Answer:

220