Problem Solving

BTGmoderatorLU wrote: ↑

Sun May 09, 2021 7:40 am

Source: Magoosh

In how many different ways can 3 fiction books and 3 non-fiction books be arranged in a row of 6 books on a shelf such that the fiction books are not separated, and the non-fiction books are not separated?


A. 24
B. 36
C. 72
D. 144
E. 288

The OA is C

Take the task of arranging the 6 books and break it into stages.

Stage 1: Arrange the 3 fiction books in a row
We can arrange n unique objects in n! ways
So, we can arrange the 3 books in 3! ways (= 6 ways)
So, we can complete stage 1 in 6 ways

Stage 2: Arrange the 3 non-fiction books in a row
We can complete stage 2 in 6 ways

Now that we've arranged the two types of books, we need to determine the order they appear on the shelf (i.e.. fiction-nonfiction or nonfiction-fiction)

Stage 3: Select the order in which the 2 book types appear on the shelf
There are 2 options: fiction-nonfiction or nonfiction-fiction
So, we can complete stage 3 in 2 ways

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus arrange all 6 books) in (6)(6)(2) ways (= 72 ways)

Answer: C