A bookstore receives six boxes of books per month on six ran

A bookstore receives six boxes of books per month on six random days of each month. Suppose that two of those boxes are from one publisher, two from another publisher, and the remaining two from a third publisher. Our goal is to compute the probability that the last two boxes of books received last month are from the same publisher.

(a) Describe the sample space, S, you would use to solve this problem. Make sure to define any notation you use to describe elements of the sample space.

(b) Compute the probability that the last two boxes of books received last month are from the same publisher.

Show all work and explaination!

Solution

A:The book is from the first publisher.

B:The book is from the second publisher.

C:The book is from the third publisher.

(a) S={AABBCC,AACCBB,AABCBC,AACBCB,AABCCB,AACBBC,BBAACC,BBCCAA,BBACAC,BBCACA,BBACCA,BBCAAC,CCAABB,CCBBAA,CCBABA,CCABAB,CCBAAB,CCABBA,ABABCC,BABACC,....}

(b)The last two places can be taken by same publisher in 3 ways while the remaining 4 places can be taken by (4!/2!) ways.

Now, total number of possible cases=6!/(2!2!2!)

Required probability= 3*(4!/2!)/(6!/(2!2!2!)) = 36/90= 2/5 =0.4