Answer:
252 ways
Step-by-step explanation:
The missing details are:
[tex]n = 10[/tex] --- total restaurants
[tex]r = 5[/tex] --- restaurants to visit
Required
The number of ways to perform the visitation
The question is an illustration of combination;
So, we have:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
This gives:
[tex]^{10}C_5 = \frac{10!}{(10 - 5)!*5!}[/tex]
[tex]^{10}C_5 = \frac{10!}{5!*5!}[/tex]
Expand
[tex]^{10}C_5 = \frac{10*9*8*7*6*5!}{5!*5*4*3*2*1}[/tex]
Cancel out 5!
[tex]^{10}C_5 = \frac{10*9*8*7*6}{5*4*3*2*1}[/tex]
[tex]^{10}C_5 = \frac{30240}{120}[/tex]
[tex]^{10}C_5 = 252[/tex]
