a resturant must choose 5 employees from 12 applicants. in how many ways can they do that?

To find the number of ways the restaurant can choose 5 employees from 12 applicants, we can use the concept of combinations.

The formula for combinations is given by:

C(n, r) = n! / (r! * (n - r)!)

Where n is the total number of items to choose from, r is the number of items to choose, and ! denotes factorial (the product of all positive integers less than or equal to a given number).

In this case, there are 12 applicants to choose from and the restaurant wants to choose 5 employees. So, applying the formula:

C(12, 5) = 12! / (5! * (12 - 5)!)

Simplifying further:

C(12, 5) = (12 * 11 * 10 * 9 * 8!) / (5! * 7!)

Now, let's calculate the factorial terms:

5! = 5 * 4 * 3 * 2 * 1 = 120
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40320

Substituting the factorial terms into the formula, we get:

C(12, 5) = (12 * 11 * 10 * 9 * 40320) / (120 * 5040)

Cancelling out common terms:

C(12, 5) = (12 * 11 * 10 * 9) / (120)

C(12, 5) = 95,040 / 120

C(12, 5) = 792

Therefore, there are 792 ways the restaurant can choose 5 employees from 12 applicants.