A student has 5 math books, 2 history books, and 4 biology books. She puts all...

A student has 5 math books, 2 history books, and 4 biology books. She puts all the books on the shelf in a random order. What is the probability that:

(a) The math books are together?

(b) The books are arranged by subject? (i.e., all books on the same subject are together).

Solutions

Expert Solution

Total number f books = 5+2+4 = 11

The student puts all the books on the shelf in a random order.

So, number of ways to do so = 11!

(a)

To put math books together we can consider all math books as a set of units. Thus 1+2+4 = 7 items can be arranged in 7! ways. Further 5 math books can be arranged in 5! ways for each of those arrangement.

So, number of ways so that math books are kept together = 7!*5!

Probability that math books are together is given by

(b)

To put all books of each subject together we have 3 sets of books (1st set of 5 math books, 2nd set of 2 history books and 3rd set of 4 biology books) which can be arranged in 3! ways. Further 5 math books can be arranged in 5! ways, 2 history books can be arranged in 2! ways and 4 biology books can be arranged in 4! ways for each of those arrangement.

So, number of ways so that all books of same subject are kept together = 3!*5!*2!*4!

Probability that all books of same subject are kept together is given by

orchestra answered 1 year ago

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