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.

a) How many distinguishable ways can you arrange these DVDs on the shelf?

b) What is the probability that the last DVD is one of the “Breaking Bad” DVDs?

c) What is the probability that the first three DVDs are “Game of Thrones”?

d) What is the probability that the “Arrested Development” DVDs are in order (but not necessarily next to each other)?

Explanation / Answer

Answer with explanation below. Please write back in case of doubts:

a. You can arrange them in (4+6+3)! = 6227020800 ways

b. There are 4 BB seasons, so 4C1 ways of choosing that in last position

The rest 12 can be arranged in 12! = 18480

SO, probability  that the last DVD is one of the “Breaking Bad” DVDs? = 4*12!/13! = 4/13

c. The probabiltiy that the first 3 are DVDs for GOT ?

= (6C3*3! *10!) /13!

= .06993

d. P(AD DVD; are in order) = P( AD DVD are in only 1 particular order) =

10 rest can be arranged in any way = 10! and the AD DVDs are arranged in 1 way.

So, 10!/13! = .000582

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