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31 Mar 2022, 07:15
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
93% (00:49) correct
7%
(00:37)
wrong
based on 74
sessions
History
Date
Time
Result
Not Attempted Yet
Doug is selecting books to read on his vacation. He must choose 1 poetry book, 1 novel, 1 self-help book, and 1 pop-up story book from his collection. If his collection includes 5 poetry books, 3 novels, 4 self-help books, and 10 pop-up story books,how many different selections are possible?
A. 22
B. 128
C. 500
D. 600
E. 1,040
A. 22
B. 128
C. 500
D. 600
E. 1,040
06 Apr 2022, 04:10
Kudos
Bookmarks
The collection from which Doug has to select, has 5 poetry books, 3 novels, 4 self-help books and 10 pop-up story books.
From these, Doug has to choose 1 book from each category. Since the order in which he chooses is not important, this is a question on Combinations, therefore, we apply the \(n_c_r\) expression to get our answer.
Number of ways to select 1 poetry book from 5 poetry books = \(5_C_1\) = 5
Number of ways to select 1 novel from 3 novels = \(3_C_1\) = 3
Number of ways to select 1 self-help book from 4 self-help books = \(4_C_1\) = 4
Number of ways to select 1 pop-up story book from 10 pop-up story books = \(10_C_1\) = 10
Since Doug has to select all of them simultaneously, we need to multiply the values as per the Fundamental Principle of counting.
Therefore, number of different selections possible = 5 * 3 * 4 * 10 = 15 * 40 = 600
The correct answer option is D.
From these, Doug has to choose 1 book from each category. Since the order in which he chooses is not important, this is a question on Combinations, therefore, we apply the \(n_c_r\) expression to get our answer.
Number of ways to select 1 poetry book from 5 poetry books = \(5_C_1\) = 5
Number of ways to select 1 novel from 3 novels = \(3_C_1\) = 3
Number of ways to select 1 self-help book from 4 self-help books = \(4_C_1\) = 4
Number of ways to select 1 pop-up story book from 10 pop-up story books = \(10_C_1\) = 10
Since Doug has to select all of them simultaneously, we need to multiply the values as per the Fundamental Principle of counting.
Therefore, number of different selections possible = 5 * 3 * 4 * 10 = 15 * 40 = 600
The correct answer option is D.
