Computer keyboard failures can be attributed to electrical defects or mechanical defects. a repair facility currently has 25 failed keyboards, 7 of which have electrical defects and 18 of which have mechanical defects.(a) how many ways are there to randomly select 6 of these keyboards for a thorough inspection (without regard to ) in how many ways can a sample of 6 keyboards be selected so that exactly three have a mechanical defect? (c) if a sample of 6 keyboards is randomly selected, what is the probability that no more than 2 of these will have an electrical defect?

The number of ways to select 6 keyboards is 177100.

The number of ways so that exactly three have a mechanical defect is 28560.

The probability that no more than 2 electrical defect is 0.806.

Step-by-step explanation:

Consider the provided information.

A repair facility currently has 25 failed keyboards, 7 of which have electrical defects and 18 of which have mechanical defects.

Part(A)

It is given that we need to find How many ways are there to randomly select 6 of these keyboards for a thorough inspection.

We need to select 6 keyboards out of 25.

Thus, the number of ways are:

Hence, the number of ways to select 6 keyboards is 177100.

Part(B)

In how many ways can a sample of 6 keyboards be selected so that exactly three have a mechanical defect?

We need to select 6 keyboards if exactly three have a mechanical defect that means the remain 3 have a electrical defect.

3 keyboard with electrical defects:

3 keyboard with mechanical defects:

This can be written as:

Thus, the number of ways so that exactly three have a mechanical defect is 28560.

Part(C)

If a sample of 6 keyboards is randomly selected, what is the probability that no more than 2 of these will have an electrical defect?

No more than 2 of these will have an electrical defect that means the number of electrical defect keyboards can be 0, 1 or 2.

P(No more than 2 electrical defect)={P(0 electrical defect)+P(1 electrical defect)+P(2 electrical defect)}

This can be written as:

Hence, the probability that no more than 2 electrical defect is 0.806.