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A certain school district has specified 5 different novels and 4 diffe

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theoryguy
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A certain school district has specified 5 different novels and 4 diffe [#permalink] New post   Updated on: 12 Nov 2018, 22:17
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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

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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?
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B

Originally posted by theoryguy on 12 Nov 2018, 20:07.
Last edited by Bunuel on 12 Nov 2018, 22:17, edited 2 times in total.
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Re: A certain school district has specified 5 different novels and 4 diffe [#permalink] New post   12 Nov 2018, 21:15
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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 \(= \frac{5!}{2!3!}*\frac{4!}{2!2!}=10*6=60\)
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Re: A certain school district has specified 5 different novels and 4 diffe [#permalink] New post   12 Nov 2018, 22:03
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theoryguy wrote:
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?


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)
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Re: A certain school district has specified 5 different novels and 4 diffe [#permalink] New post   13 Nov 2018, 08:04
A straight combination problem : 5c3 * 4c2 = 10 * 6 = 60 .....Ans B
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Re: A certain school district has specified 5 different novels and 4 diffe [#permalink] New post   18 Sep 2020, 06:59
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theoryguy wrote:
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

Solution:

The number of ways to choose 3 novels from 5 is 5C3 = (5 x 4 x 3)/(3 x 2) = 10, and the number of ways to choose 2 non-fiction books from 4 is 4C2 = (4 x 3)/2 = 6. Therefore, the number of ways to choose 3 novels and 2 non-fiction books is 10 x 6 = 60.

Answer: B
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Re: A certain school district has specified 5 different novels and 4 diffe [#permalink]
18 Sep 2020, 06:59
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