Question

Inspecting Restaurants How many different ways can a city health department inspector visit restaurants in a city with restaurants?

Answer 1

Answer:

252 ways

Step-by-step explanation:

The missing details are:

$n = 10$ --- total restaurants

$r = 5$ --- restaurants to visit

Required

The number of ways to perform the visitation

The question is an illustration of combination;

So, we have:

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

This gives:

$^{10}C_5 = \frac{10!}{(10 - 5)!*5!}$

$^{10}C_5 = \frac{10!}{5!*5!}$

Expand

$^{10}C_5 = \frac{10*9*8*7*6*5!}{5!*5*4*3*2*1}$

Cancel out 5!

$^{10}C_5 = \frac{10*9*8*7*6}{5*4*3*2*1}$

$^{10}C_5 = \frac{30240}{120}$

$^{10}C_5 = 252$