Computer keyboard failures can be attributed to electrical defects or mechanical

Question

Computer keyboard failures can be attributed to electrical defects or mechanical defects. A repair facility currently has 25 failed keyboards, 8 of which have electrical defects and 17 of which have mechanical defects How many ways are there to randomly select 7 of these keyboards for a thorough inspection (without regard to order)? 480700 (a) which hav ways mechani (b) In how many ways can a sample of 7 keyboards be selected so that exactly two have an electrical defect? ways (c) If a sample of 7 keyboards is randomly selected, what is the probability that at least 6 of these will have a mechanical defect? (Round your answer to four decimal places.)

Explanation / Answer

Solution:-
a) C(n,r) = C(25,7)
= 25!/(7!(257)!)
= 480700

b) Number of ways of selecting 2 keyboards out of 8 that have electrical defects is
C(n,r) = C(8,2) = 28
Number of ways of selecting 5 keyboards out of 17 that have mechanical defects is
C(n,r) = C(17,5) = 6188
So number of ways can a sample of 7 keyboards be selected so that exactly two have an electrical defect is
=> 28*6188 = 173264

c) Number of ways of selecting 6 keyboards that have mechanical defects is
C(17,6) (8,1) = 12376*8 = 99008

Number of ways of selecting 7 keyboards that have mechanical defects is
C(17,7) = 19448

So the number of ways of selecting at least 6 that have a mechanical defect is
99008+19448 = 118456

=> Therefore the probability that at least 6 of these will have a mechanical defect will be
118456/480700 = 0.2464

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