• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 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 cricket team consisting of 5 batsmen, 4

This topic has 3 expert replies and 0 member replies

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

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



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 allrounders?

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

OA D

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
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 allrounders?

A. 567
B. 1420
C. 2256
D. 2835
E. 5670
From 7 batsmen, the number of ways to choose 5 = 7C5 = (7*6*5*4*3)/(5*4*3*2*1) = 21.
From 6 bowlers, the number of ways to choose 4 = 6C4 = (6*5*4*3)/(4*3*2*1) = 15.
From 3 wicketkeepers, the number of ways to choose 1 = 3.
From 3 allrounders, the number of ways to choose 1 = 3.
To combine these options, we multiply:
21*15*3*3 = integer with a units digit of 5.

The correct answer is D.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

GMAT/MBA Expert

Post
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 allrounders?

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

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for our free Question of the Day emails
And check out all of our free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
Post
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 allrounders?

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

OA D
The 5 batsmen can be chosen in 7C5 ways. The 4 bowlers can be chosen in 6C4 ways. One wicketkeeper and one all-rounder each can be chosen in 3C1 ways. In total, the team can be chosen in

7C5 x 6C4 x 3C1 x 3C1 = 7!/(5!2!) x 6!/(4!2!) x 3 x 3 = [(7 x 6)/2] x [(6x5)/2] x 3 x 3

= 7 x 3 x 3 x 5 x 3 x 3 = 2835

ways.

Answer: D

_________________

Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com



See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

  • +1 Upvote Post
  • Quote
  • Flag
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep

Top First Responders*

1 Jay@ManhattanReview 71 first replies
2 Brent@GMATPrepNow 67 first replies
3 GMATGuruNY 43 first replies
4 Ian Stewart 27 first replies
5 Scott@TargetTestPrep 18 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

221 posts
2 image description Max@Math Revolution

Math Revolution

93 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

90 posts
4 image description Jay@ManhattanReview

Manhattan Review

73 posts
5 image description GMATGuruNY

The Princeton Review Teacher

66 posts
See More Top Beat The GMAT Experts