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B
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Difficulty:
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Question Stats:
83% (01:08) correct
17%
(01:43)
wrong
based on 210
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A certain school district has specified 5 different novels and 4 different non-fiction books from which teachers can choose to assemble a summer reading list. Each summer reading list must have exactly 3 novels and 2 non-fiction books. How many different summer reading lists are possible?
A) 54
B) 60
C) 72
D) 120
E) 240
A) 54
B) 60
C) 72
D) 120
E) 240
I thought it would be 5!P2! X 4!P2! but that's not even an answer. I'm a bit stuck on how to proceed. Thoughts?
12 Nov 2018, 21:15
Kudos
Bookmarks
OA: B
Number of choosing \(3\) different novels out of \(5\) novels \(= C(5,3) = \frac{5!}{2!3!}\)
Number of choosing \(2\) different non fiction out of \(4\) non fiction books \(= C(4,2) = \frac{4!}{2!2!}\)
Number of different reading list possible \(= \frac{5!}{2!3!}*\frac{4!}{2!2!}=10*6=60\)
Number of choosing \(3\) different novels out of \(5\) novels \(= C(5,3) = \frac{5!}{2!3!}\)
Number of choosing \(2\) different non fiction out of \(4\) non fiction books \(= C(4,2) = \frac{4!}{2!2!}\)
Number of different reading list possible \(= \frac{5!}{2!3!}*\frac{4!}{2!2!}=10*6=60\)
12 Nov 2018, 22:03
Kudos
Bookmarks
theoryguy
A certain school district has specified 5 different novels and 4 different non-fiction books from which teachers can choose to assemble a summer reading list. Each summer reading list must have exactly 3 novels and 2 non-fiction books. How many different summer reading lists are possible?
A)54
B)60
C)72
D)120
E)240
I thought it would be 5!P2! X 4!P2! but that's not even an answer. I'm a bit stuck on how to proceed. Thoughts?
A)54
B)60
C)72
D)120
E)240
I thought it would be 5!P2! X 4!P2! but that's not even an answer. I'm a bit stuck on how to proceed. Thoughts?
Note that this is a selection, not an arrangement. It means you have to select 3 novels out of 5 AND 2 non fiction out of 4. You DO NOT have to arrange the total 5 books you selected in a row. You are not looking for arrangements. You use 5P3 when you want to select and arrange 3 books out of 5.
When only selection is required, you use 5C3 and 4C2.
No of ways = 5C3 * 4C2 = 5!/3!*2! * 4!/2!*2! = 10*6 = 60
Answer (B)
