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Tue Jan 19, 2021 2:49 am

Magoosh

Lyndsy has six novels she wants to read, one of which is Emma, she plans to create a reading list of four of these novels for an upcoming trip, and different orders count as different lists. How many readings list are possible if Emma has to be on the list?

A. 60
B. 120
C. 240
D. 360
E. 6

OA C

Solution:

Since Emma is one of the four books, the number of ways she can choose 3 from the remaining 5 books is 5C3 = (5 x 4 x 3) / 3!. Once she has her choice of 4 books, she can arrange each set of 4 books in 4! ways. Therefore, the number of possible lists is:

[(5 x 4 x 3) / 3!] x 4! = 5 x 4 x 3 x 4 = 240

Alternate Solution:

First, let’s find the number of ways to read the novels if she reads Emma first. She must choose and order 3 novels from the remaining 5, and there are 5P3 = 5!/(5-3)! = 5 x 4 x 3 = 60 different ways of doing this.

Next, we observe that we can take any one of the 60 ways worked out above and move Emma from the first position to the second, third, or fourth positions. Each of these will correspond to a different ordered list of novels, and, together with the lists where Emma was the first book, there are 60 x 4 = 240 different lists of books.

Answer: C