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# 10 different biology books and 8 different chemistry books lie on a sh

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Math Expert
Joined: 02 Sep 2009
Posts: 52906
10 different biology books and 8 different chemistry books lie on a sh  [#permalink]

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09 Oct 2016, 23:47
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4
00:00

Difficulty:

35% (medium)

Question Stats:

66% (01:29) correct 34% (01:22) wrong based on 244 sessions

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10 different biology books and 8 different chemistry books lie on a shelf. In how many ways can a student pick 2 books of each type?

A. 80
B. 160
C. 720
D. 1100
E. 1260

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Re: 10 different biology books and 8 different chemistry books lie on a sh  [#permalink]

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10 Oct 2016, 00:56
3
No. of ways of picking 2 biology books(from 10 books) = 10c2 = (10*9)/2 = 45
No. of ways of picking 2 chemistry books(from 8 books) = 8c2 = (8*7)/2 = 28

Total ways of picking 2 books of each type = 45*28 =1260(Option E)
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10 different biology books and 8 different chemistry books lie on a sh  [#permalink]

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10 Oct 2016, 04:47
Bunuel wrote:
10 different biology books and 8 different chemistry books lie on a shelf. In how many ways can a student pick 2 books of each type?

A. 80
B. 160
C. 720
D. 1100
E. 1260

The Highlighted part suggests that in each drawing of Books the student must pick both books of the same subject..

So, The possible ways = $$(10C2)$$*$$(8C2)$$ = 28*45 => 1260

So, Answer will be (E) 1260

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Re: 10 different biology books and 8 different chemistry books lie on a sh  [#permalink]

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17 Nov 2016, 17:29
Simple.

10C2 x 8C6 = 1260
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Re: 10 different biology books and 8 different chemistry books lie on a sh  [#permalink]

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29 Nov 2016, 15:30
Bunuel wrote:
10 different biology books and 8 different chemistry books lie on a shelf. In how many ways can a student pick 2 books of each type?

A. 80
B. 160
C. 720
D. 1100
E. 1260

We are given that there are 10 different biology books and 8 different chemistry books. We must determine in how many ways a student can select 2 books of each type.

Number of ways to select 2 biology books is 10C2 = (10 x 9)/2! = 45.

Number of ways to select 2 chemistry books is 8C2 = (8 x 7)/2! = 28.

Thus, the number of ways to select 2 books of each type is 45 x 28 = 1,260.

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Re: 10 different biology books and 8 different chemistry books lie on a sh  [#permalink]

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03 Jan 2017, 04:19
Pick up Biology 10!/2!8! =45
Pick up Chemistry 8!/2!6! =28
Now we should multiply as we have to select 2 books from Biology AND Chemistry
in combination AND means multiply
so 45*28 =1260
Option E
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Re: 10 different biology books and 8 different chemistry books lie on a sh  [#permalink]

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21 Jan 2019, 06:35
Top Contributor
Bunuel wrote:
10 different biology books and 8 different chemistry books lie on a shelf. In how many ways can a student pick 2 books of each type?

A. 80
B. 160
C. 720
D. 1100
E. 1260

Take the task of selecting 4 books and break it into stages.

Stage 1: Select two biology books
Since the order in which we select the books does not matter, we can use combinations.
We can select 2 books from 10 books in 10C2 ways (45 ways)
So, we can complete stage 1 in 45 ways

If anyone is interested, the video below explains how to calculate combinations (like 10C2) in your head

Stage 2: Select two chemistry books
We can select 2 books from 8 chemistry books in 8C2 ways (28 ways)
So, we can complete stage 2 in 28 ways

By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus select 4 books) in (45)(28) ways (= 1260 ways)

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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Re: 10 different biology books and 8 different chemistry books lie on a sh   [#permalink] 21 Jan 2019, 06:35
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