Question

The general manager of a fast food restaurant chain must select 3 restaurants from 18 for a promotional program how many different possible ways can this selection be done

Answer 1

Considering that the order of restaurants does not matter, we use Combination and solve using the formula below. The combination of n thing taken r at a time is:

$^nC_r=\frac{n!}{r!(r-n)!}$

In this question:

n = 18

r = 3

Substituting the values in the formula:

$\begin{gathered} ^nC_r=\frac{18!}{3!*(18-3)!} \\ ^nC_r=\frac{18*17*16*15!}{3*2*15!} \\ ^nC_r=\frac{18*17*16}{6} \\ ^nC_r=816 \end{gathered}$

Answer:

1) 816 ways.