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:
[tex]^nC_r=\frac{n!}{r!(r-n)!}[/tex]
In this question:
n = 18
r = 3
Substituting the values in the formula:
[tex]\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}[/tex]
Answer:
1) 816 ways.
