Question

in how many ways can you select 3 books to bring on vacation from a group of 11 books?

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

Explanation:

Identify the parameters

$$ n = 11, \quad r = 3 $$

Apply the combination formula

$$ _{11}C_3 = \frac{11!}{3!(11-3)!} = \frac{11!}{3! \cdot 8!} $$

Simplify and calculate

$$ _{11}C_3 = \frac{11 \times 10 \times 9}{3 \times 2 \times 1} = 165 $$

Answer:

165