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In how many ways a criket team consisting of 5 batsmen, 4

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In how many ways a criket team consisting of 5 batsmen, 4

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e-GMAT

In how many ways a cricket team consisting of 5 batsmen, 4 bowlers, and 1 wicketkeeper and 1 all-rounder can be selected from the pool of 7 batsmen, 6 bowlers, 3 wicketkeepers and 3 all-rounders?

A. 567
B. 1420
C. 2256
D. 2835
E. 5670

OA D

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AAPL wrote:
e-GMAT

In how many ways a cricket team consisting of 5 batsmen, 4 bowlers, and 1 wicketkeeper and 1 all-rounder can be selected from the pool of 7 batsmen, 6 bowlers, 3 wicketkeepers and 3 all-rounders?

A. 567
B. 1420
C. 2256
D. 2835
E. 5670

OA D
Take the task of creating a cricket team and break it into stages.

Stage 1: Select 5 batsmen
Since the order in which we select the batsmen does not matter, we can use combinations.
We can select 5 batsmen from 7 batsmen in 7C5 ways (21 ways)
So, we can complete stage 1 in 21 ways

Stage 2: Select 4 bowlers
Since the order in which we select the bowlers does not matter, we can use combinations.
We can select 4 bowlers from 6 bowlers in 6C2 ways (15 ways)
So, we can complete stage 2 in 15 ways

Stage 3: Select 1 wicketkeeper
There are 3 wicketkeepers from which to choose, so we can complete this stage in 3 ways.

Stage 4: Select 1 all-rounder
There are 3 all-rounders from which to choose, so we can complete this stage in 3 ways.

By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus create a cricket team) in (21)(15)(3)(3) ways ( = 2835 ways)

Answer: D
--------------------------

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

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

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should-be-the-answer-t267256.html
- https://www.beatthegmat.com/counting-problem-company-recruitment-t244302.html
- https://www.beatthegmat.com/picking-a-5-digit-code-with-an-odd-middle-digit-t273110.html
- https://www.beatthegmat.com/permutation-combination-simple-one-t257412.html
- https://www.beatthegmat.com/simple-one-t270061.html


MEDIUM
- https://www.beatthegmat.com/combinatorics-solution-explanation-t273194.html
- https://www.beatthegmat.com/arabian-horses-good-one-t150703.html
- https://www.beatthegmat.com/sub-sets-probability-t273337.html
- https://www.beatthegmat.com/combinatorics-problem-t273180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-separator-method-t271047.html
- https://www.beatthegmat.com/combinatorics-problem-t267079.html


DIFFICULT
- https://www.beatthegmat.com/wonderful-p-c-ques-t271001.html
- https://www.beatthegmat.com/permutation-and-combination-t273915.html
- https://www.beatthegmat.com/permutation-t122873.html
- https://www.beatthegmat.com/no-two-ladies-sit-together-t275661.html
- https://www.beatthegmat.com/combinations-t123249.html


Cheers,
Brent

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Brent Hanneson – Creator of GMATPrepNow.com
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