Question

Here is my question please show all of your work and answer as well

A shipment of 12 X-Ray machines includes 4 that are defective. In how many ways can a hospital purchase 5 of these machines and receive at least 2 of the defective machines

Answer 1

Explanation:

The number of ways the hospital can purchase 5 machines and receive at least 2 of the defective machines is calculated as follows:

The number of ways the hospital can receive exactly 2 defective machines is C(4,2) = 6, where C(n, k) is the number of combinations of n things taken k at a time.

The number of ways the hospital can receive exactly 3 defective machines is C(4,3) = 4.

The number of ways the hospital can receive exactly 4 defective machines is C(4,4) = 1.

So, the total number of ways the hospital can purchase 5 machines and receive at least 2 of the defective machines is 6 + 4 + 1 = 11.