5. Nine smart phones have just been received at an authorized service center. Th

Question

5. Nine smart phones have just been received at an authorized service center. Three of these tele- phones are iPhones, Three are Galaxv phones, and the other three are Windows phones. Suppose that these phones are randomly allocated the numbers 1,2,... ,9 to establish the order in which they will be serviced. Note that because these phones are in service (rather than new out of the box), phones of the same type are not interchangeable! (a) What is the probability that all the iPhones are among the first six to be serviced? (b) What is the probability that after servicing six smart phones, phones of only one of the three types remain to be serviced?

Explanation / Answer

A) P(all the iPhones are among the first 6 to be serviced) = 6C6/9C6

= 1/84

= 0.0119

b) P(one type remains after 6 smart phones are serviced) = P(3 iPhones and 3 galaxy) + P(3iPhones and 3 windows) + P(3 galaxy and 3 windows) + P(6 iPhones)

= (6C3x3C3/9C6) + (6C3x3C3/9C6) + (3C3x3C3/9C6) + (6C6/9C6)

= 1/84 + 20/84 + 1/84 + 1/84

= 23/84

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