BTGModeratorVI wrote: ↑

Sun Jul 19, 2020 1:35 pm

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

Answer: E
Source: Economist GMAT

Required no. of ways = 10C2*8C2 = [10.9/1.2]*[8.7/1.2] = 45*28 = 1,260

Correct answer: E

Hope this helps!

-Jay
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BTGModeratorVI wrote: ↑

Sun Jul 19, 2020 1:35 pm

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

Answer: E
Source: Economist GMAT

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)

Answer: E

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch this video: https://www.gmatprepnow.com/module/gmat- ... /video/775

You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat ... /video/776

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
- https://www.beatthegmat.com/counting-pro ... 44302.html
- https://www.beatthegmat.com/picking-a-5- ... 73110.html
- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html


MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
- https://www.beatthegmat.com/arabian-hors ... 50703.html
- https://www.beatthegmat.com/sub-sets-pro ... 73337.html
- https://www.beatthegmat.com/combinatoric ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
- https://www.beatthegmat.com/combinatoric ... 67079.html


DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
- https://www.beatthegmat.com/permutation- ... 73915.html
- https://www.beatthegmat.com/permutation-t122873.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/combinations-t123249.html


Cheers,
Brent