We have a batch of 100 pieces of which 20 are defective. 10 pieces are chosen...

Question

Question

We have a batch of 100 pieces of which 20 are defective. 10 pieces are chosen at random.

a) In how many ways can the 10 pieces be chosen?

b) In how many ways can we choose 2 defective pieces and 8 good ones?

Answer 1

Answer #1

Number of ways to select r items from n, nCr = n!/(r! x (n-r)!)

a) Number of ways 10 pieces can be chosen = 100C10

= 100!/(10! x 90!)

= 1.731x1013

b) Number of defective = 20

Number of good ones = 100 - 20 = 80

Number of ways to choose 2 defective pieces and 8 good ones = 20C2 x 80C8

= 190 x 2.899x1010

= 5.508x1012

Answer 2

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