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# Clarissa wants to buy 5 books from the 10 books available on a websit

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2888
Clarissa wants to buy 5 books from the 10 books available on a websit  [#permalink]

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Updated on: 13 Aug 2018, 07:08
00:00

Difficulty:

45% (medium)

Question Stats:

64% (01:48) correct 36% (01:32) wrong based on 165 sessions

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Fool-proof method to Differentiate between Permutation & Combination Questions - Exercise Question #4

4- Clarissa wants to buy 5 books from the 10 books available on a website. She will then place all the 5 books in her library in the order they are chosen. In how many ways can she place the books in the library.

Options:
A. 120
B. 252
C. 2520
D. 3024
E. 30240

Learn to use the Keyword Approach in Solving PnC question from the following article:

Article-1: Learn when to “Add” and “Multiply” in Permutation & Combination questions

Article-2: Fool-proof method to Differentiate between Permutation & Combination Questions

_________________

Originally posted by EgmatQuantExpert on 11 Apr 2018, 23:17.
Last edited by EgmatQuantExpert on 13 Aug 2018, 07:08, edited 4 times in total.
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Posts: 2888
Clarissa wants to buy 5 books from the 10 books available on a websit  [#permalink]

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Updated on: 26 Nov 2018, 02:03

Solution

Given:
• Clarissa wants to 5 books from 10 books.
• She will then place all the books in order as the books are chosen.

To find:
• The number of ways in which Clarissa can order the 5 books in her library.
Approach and Working:

• She is first selecting 5 books and then ordering them in the library.
• This is same as selectin and then arrangement.
o Hence, this a permutation question.
• Thus, total ways= $$^{10}P_5$$= 30240.

Hence, option E is the correct answer.

_________________

Originally posted by EgmatQuantExpert on 11 Apr 2018, 23:20.
Last edited by EgmatQuantExpert on 26 Nov 2018, 02:03, edited 2 times in total.
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Joined: 26 Feb 2016
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Re: Clarissa wants to buy 5 books from the 10 books available on a websit  [#permalink]

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11 Apr 2018, 23:34
EgmatQuantExpert wrote:
Learn the structured approach to identify permutation and combination question - Exercise Question #4

4- Clarissa wants to buy 5 books from the 10 books available on a website. She will then place all the 5 books in her library in the order they are chosen. In how many ways can she place the books in the library.

Options:
A. 120
B. 252
C. 2520
D. 3024
E. 30240

Clarissa can pick 5 books from the 10 books available in $$C_5^{10} = \frac{10!}{5!*5!}$$ ways.

She can now place all the books in her library in 5! ways.

Therefore, the books can be chosen in $$\frac{10!}{5!*5!} * 5! = 30240$$ ways (Option E)
_________________
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Re: Clarissa wants to buy 5 books from the 10 books available on a websit  [#permalink]

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17 Apr 2018, 09:02
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Joined: 25 Nov 2017
Posts: 86
Location: India
GMAT 1: 590 Q47 V25
GMAT 2: 660 Q50 V29
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Re: Clarissa wants to buy 5 books from the 10 books available on a websit  [#permalink]

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25 Nov 2018, 05:13
Clarissa can choose 5 books from 10 books in 10C5 ways.When she arranges the books in the order they are chosen,this order should always be one for a particular selection of 10C5 selections.
@e-GMAT , plz help understanding this.
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Posts: 2888
Re: Clarissa wants to buy 5 books from the 10 books available on a websit  [#permalink]

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26 Nov 2018, 02:06
Re: Clarissa wants to buy 5 books from the 10 books available on a websit   [#permalink] 26 Nov 2018, 02:06
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