Computer keyboard failures can be attributed to electrical defects or mechanical defects. A repair facility currently has 25 failed keyboards, 6 of which have electrical defects and 19 of which have mechanical defects. a. ?How many ways are there to randomly select 5 of these keyboards for a thorough inspection (without regard to order)? b. ?In how many ways can a sample of 5 keyboards be selected so that exactly two have an electrical defect? c. ?If a sample of 5 keyboards is randomly selected, what is the probability that at least 4 of these will have a mechanical defect?

Answer: Step 1: Computer keyboard failures can be attributed to electrical defects or mechanical defects. A repair facility currently has 25 failed keyboards, 6 of which have electrical defects and 19 of which have mechanical defects. Step 2: a). Here we have to find how many ways are there to randomly select 5 of these keyboards for a thorough inspection (without regard to order). Number of ways to select 5 out of 25 is 25 c5= 53130 Therefore, 53130 ways are there to randomly select 5 of these keyboards for a thorough inspection.