Assume that all the books in this problem are distinct, Suppose I have 40 mathem

Question

Assume that all the books in this problem are distinct, Suppose I have 40 mathematics books, 40 physics, 40 chemistry books, and 40 biology book. The following are two different ways to compute the number of ways in which in which this can be done. Pick a mathematics book (40 ways), pick a physics books (40 ways), pick a chemistry book (40 ways), pick a biology book (40 ways), and then pick a fifth book from remaining 156 books (156 ways). Therefore, answer-1 - 40 x 40 x 40 x 40 x 156. Approach 2: The collection must have 2 books from one subject and a book each from the remaining 3 subjects. Construct such a collection as follows: pick the subject that contributes 2 books (C(4, 1) ways), pick 2 books from that subject (C(40, 2) ways), pick a book from each of the remaining subjects (C(40, 1) x C(40, 1) x C(40, 1) ways). Therefore, answer-2 = C(4,1) x C(40,2) x C(40,1) x C(40, l) x i). Exactly one of the two answers is correct. Which one is it ? Compute the actual values of answer-1 and answer-2 and comment on how the two values relate numerically. that way.

Explanation / Answer

a. Approach 1 is right.

b.

Answer 1 : 399360000

Answer 2 : 199680000

Answer 1 = 2 X Answer 2

c.

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