Problem 2 (3 points) Alan has moved to a new apartment. He owns five math (M) bo

Q: Problem 2 (3 points) Alan has moved to a new apartment. He owns five math (M) bo

Let us assume books of the same subject are identical Lets us assume that books of each subject comprise a group. Hence, total number of groups = 3 (M, E and P) Number of ways of arranging these = 3! = 6 Total number of ways of arranging 12 books (out of which 5, 4 and 3 are identical to each other) = 12! / (5! * 4! * 3!) = 27720 Probability that books of same subject are kept together = 6 / 27720 = 0.000216

ID: 3070691 • Letter: P

Question

Problem 2 (3 points) Alan has moved to a new apartment. He owns five math (M) books, three physics (P) Pbooks, and four engineering (E) books. Prior to moving, Alan has put these books into a moving box uniformly at random. While unpacking at his new home, he puts these books back onto a shelf. Compute the probability that the new arrangement of books on the shelf is grouped by subjects, i.e., all math books are next to each other, all physics books are next to teach other, and ll engineering books are next to each other. Examples:

Explanation / Answer

Let us assume books of the same subject are identical

Lets us assume that books of each subject comprise a group.

Hence, total number of groups = 3 (M, E and P)

Number of ways of arranging these = 3! = 6

Total number of ways of arranging 12 books (out of which 5, 4 and 3 are identical to each other)

= 12! / (5! * 4! * 3!)

= 27720

Probability that books of same subject are kept together = 6 / 27720

= 0.000216

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Problem 2 (3 points) Alan has moved to a new apartment. He owns five math (M) bo

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