You have many DVDs to organize on a shelf near your television. You have 4 seaso

Question

You have many DVDs to organize on a shelf near your television. You have 4 seasons of "Breaking Bad", 6 seasons of "Game of Thrones" and 3 seasons of "Arrested Development". Each season is recorded on a single DVD and is clearly labeled. How many distinguishable ways can you arrange these DVDs on the shelf? What is the probability that the last DVD is one of the "Breaking Bad" DVDs? What is the probability that the first three DVDs are "Game of Thrones"? What is the probability that the "Arrested Development" DVDs are in order (but not necessarily next to each other)? a) b) c) d)

Explanation / Answer

As each show and respective seasons are distinguishable

a)

Total ways to arrange the DVDs are (4+6+3)! = 13! = 6227020800

b)

Ways to arrange DVDS so that the last DVD is breaking bad = 4*12! =1916006400

Prob = 4/13

c)

Ways in which first 3 game of thrones can be arranged= selecting 3 of 6 = P(6,3) = 120

Ways in which rest 10 DVDs can be arranged = 10!

Total ways = 120*10!

Prob = (120*10!)/13! = 0.07

d)

ways to arrange arrested development DVDs in order = (1/6)*13! = 1037836800

Prob = 1/6

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