• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

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

This topic has expert replies
Moderator
Posts: 1371
Joined: 29 Oct 2017
Followed by:2 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 14498
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1262 members
GMAT Score:770

by Brent@GMATPrepNow » Fri Mar 29, 2019 6:09 am
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: 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
Use my video course along with Beat The GMAT's free 60-Day Study Guide
Image
Watch these video reviews of my course
And check out these free resources