Question

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

Answer 1

252 ways

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

This gives:

`^(10)C_5 = (10!)/((10 - 5)!*5!)`

`^(10)C_5 = (10!)/(5!*5!)`

Expand

`^(10)C_5 = (10*9*8*7*6*5!)/(5!*5*4*3*2*1)`

Cancel out 5!

`^(10)C_5 = (10*9*8*7*6)/(5*4*3*2*1)`

`^(10)C_5 = (30240)/(120)`

`^(10)C_5 = 252`