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10 different biology books and 8 different chemistry books l

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by BTGmoderatorDC » Mon Jan 21, 2019 1:03 am

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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

OA E

Source: Economist Gmat
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10 different biology books and 8 different chemistry books l

by fskilnik@GMATH » Mon Jan 21, 2019 4:31 am
BTGmoderatorDC 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
Source: Economist Gmat
$$? = C\left( {10,2} \right) \cdot C\left( {8,2} \right) = \left( {\frac{{10 \cdot 9}}{2}} \right) \cdot \left( {\frac{{8 \cdot 7}}{2}} \right) = 45 \cdot 28 = \underleftrightarrow {45 \cdot \left( {30 - 2} \right) = 1350 - 90} = 1260$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by Brent@GMATPrepNow » Mon Jan 21, 2019 6:19 am
BTGmoderatorDC 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, we have a free video on calculating combinations (like 10C2) in your head: https://www.gmatprepnow.com/module/gmat ... /video/775

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Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by swerve » Mon Jan 21, 2019 9:30 am
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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by Scott@TargetTestPrep » Sun Jan 27, 2019 9:46 am
BTGmoderatorDC 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

OA E

Source: Economist Gmat
Since the order in which the books are selected does not matter, we have a combination problem. Let's start by determining the number of ways to select the biology books.

Number of ways to select the biology books = 10C2 = 10!/(2! x 8!) = (10 x 9)/2! = 5 x 9 = 45.

Next we can determine the number of ways to select the chemistry books.

Number of ways to select the chemistry books = 8C2 = 8!/(2! x 6!) = (8 x 7)/2! = 4 x 7 = 28.

Thus, the number of ways to select 2 biology books and 2 chemistry books is 45 x 28 = 1,260.

Answer: E

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