**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

00:00

**A**

**B**

**C**

**D**

**E**

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

- Brent@GMATPrepNow
- GMAT Instructor
**Posts:**15002**Joined:**08 Dec 2008**Location:**Vancouver, BC**Thanked**: 5254 times**Followed by:**1265 members**GMAT Score:**770

Take the task of creating a cricket team and break it intoAAPL 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

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

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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: 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-pr ... 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/combinatori ... 73194.html

- https://www.beatthegmat.com/arabian-hor ... 50703.html

- https://www.beatthegmat.com/sub-sets-pr ... 73337.html

- https://www.beatthegmat.com/combinatori ... 73180.html

- https://www.beatthegmat.com/digits-numbers-t270127.html

- https://www.beatthegmat.com/doubt-on-se ... 71047.html

- https://www.beatthegmat.com/combinatori ... 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-ladi ... 75661.html

- https://www.beatthegmat.com/combinations-t123249.html

Cheers,

Brent

Brent Hanneson - Creator of GMATPrepNow.com

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