A programming director has 22 television shows to fill 8 slots between 6:00 pm a

Question

A programming director has 22 television shows to fill 8 slots between 6:00 pm and 10:00 pm. Of the 22 shows, 9 are sitcoms, 7 are news programs, and 6 are reality shows.

(a) How many different line-ups are possible?

(b) Station executives have decided that 3 of the 8 time slots must be reality shows. Without regard to order, how many different groups of reality shows are possible?

(c) Given that 3 of the 8 slots must be reality shows and 2 of the 8 must be news programs, what is the probability that the remaining 3 slots are all sitcoms?

Explanation / Answer

(a) Number of line-ups possible = 22P8

= 22!/(22-8)!

= 1.289x1010

(b) Number of groups of reality shows possible = 6C3 = 6!/(3! x (6-3)!)

= 20

(c) Number of options remaining = 22-5 = 17

Number of sitcoms = 9

P(remaining 3 shows are sitcoms) = 9C3/17C3

= 0.12353

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