Question

A quality control inspector samples 2 computer chips from a box containing 13 computer chips. If the box contains 3 defective chips, in how many ways can he select a sample so that at least one of the chips is defective?

Answer 1

The number of ways to select a sample of 2 computer chips so that at least one of the chips is defective is 33 ways.

Explanation:

The box contains 13 computer chips. Of these 13 chips 3 are defective and 10 are good.

A quality control inspector samples 2 computer chips.

The number of ways to select at least 1 defective chip is:

n (At least 1 defective chip) = n (1 defective chip) + n (2 defective chips)

The number of ways to select 1 defective chip is:
`{3\choose 1}{10\choose 1}=3*10=30` ways.

The number of ways to select 2 defective chips is:
`{3\choose 2}{10\choose 0}=3*1=3` ways.

n (At least 1 defective chip) = n (1 defective chip) + n (2 defective chips)

= 30 + 3

= 33

Thus, the number of ways to select a sample of 2 computer chips so that at least one of the chips is defective is 33 ways.