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=(n!)/(r!(r-n)!)`

In this question:

n = 18

r = 3

Substituting the values in the formula:

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

Answer:

1) 816 ways.