Question

There are 15 books on a shelf, 5 of which are on fiction. If five books are selected at random, find the probability that 4 of them are books on fiction.

• A. 5/72
• B. 5/273
• C. 50/3003
• D. 50/273
• E. None of these

Answer 1

The Correct Option is C

The correct answer is option (C):

50/3003

Let's break down how to solve this probability problem. We're dealing with combinations since the order in which we select the books doesn't matter.

First, we need to find the total number of ways to select 5 books out of 15. This is given by the combination formula:

C(n, k) = n! / (k! * (n-k)!)

where n is the total number of items, and k is the number of items we are choosing.

In our case, n = 15 (total books) and k = 5 (books selected).

Total possible combinations = C(15, 5) = 15! / (5! * 10!) = (15 * 14 * 13 * 12 * 11) / (5 * 4 * 3 * 2 * 1) = 3003

Now, let's find the number of ways to select 4 fiction books and 1 non-fiction book. We have 5 fiction books, and we want to choose 4 of them. Also, we have 10 non-fiction books (15 total - 5 fiction), and we want to choose 1.

Ways to choose 4 fiction books = C(5, 4) = 5! / (4! * 1!) = 5

Ways to choose 1 non-fiction book = C(10, 1) = 10! / (1! * 9!) = 10

To get the number of ways to choose 4 fiction and 1 non-fiction, we multiply these two results:

Favorable combinations = C(5, 4) * C(10, 1) = 5 * 10 = 50

Finally, to find the probability, we divide the number of favorable combinations by the total possible combinations:

Probability = (Favorable combinations) / (Total possible combinations) = 50 / 3003

Therefore, the probability of selecting 4 fiction books when selecting 5 books at random is 50/3003. This matches the provided correct answer.