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

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Joined: 04 Jan 2015
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In how many ways a cricket team consisting of 5 batsmen, 4 bowlers, an [#permalink]

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Updated on: 17 Apr 2018, 01:39
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Fool-proof method to Differentiate between Permutation & Combination Questions - Exercise Question #1

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.

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

Learn to use the Keyword Approach in Solving PnC question from the following article:

Article-1: Learn when to “Add” and “Multiply” in Permutation & Combination questions

Article-2: Fool-proof method to Differentiate between Permutation & Combination Questions
[Reveal] Spoiler: OA

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Originally posted by EgmatQuantExpert on 11 Apr 2018, 23:06.
Last edited by EgmatQuantExpert on 17 Apr 2018, 01:39, edited 3 times in total.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 1001
In how many ways a cricket team consisting of 5 batsmen, 4 bowlers, an [#permalink]

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Updated on: 17 Apr 2018, 08:47

Solution

Given:

• We need to select a cricket team i.e. 11 players
o We need to select 5 batsmen from 7 batsmen and,
o We need to select 4 bowlers from 6 bowlers and,
o We need to select 1 wicket keeper from 3 wicket keepers and,
o We need to select 1 all-rounder from 3 all-rounders.

To find:
• The number of ways we can from a cricket team out of 7 batsmen, 6 bowlers, 3 allrounders and 3 wicketkeepers available.

Approach and Working:

Since we need to select 5 batsmen, 4 bowlers, and 1 wicket keeper and 1 all-rounder in the cricket team,
• Hence, number of ways to form the cricket team= ways to select 5 batsmen from 7 batsmen* ways to select 4 bowlers from 6 bowlers * ways to select 1 wicket keeper from 3 wicket keepers * ways to select 1 all-rounder from 3 all-rounders

• Thus, total ways= $$^7c_5$$*$$^6c_4$$*$$^3c_1$$*$$^3c_1$$

• =21*15*3*3= 2835

Hence, in 2835 ways we can select a cricket team.

Hence, option D is the correct answer.

Answer: D
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Originally posted by EgmatQuantExpert on 11 Apr 2018, 23:19.
Last edited by EgmatQuantExpert on 17 Apr 2018, 08:47, edited 1 time in total.
Intern
Joined: 03 Aug 2016
Posts: 34
Re: In how many ways a cricket team consisting of 5 batsmen, 4 bowlers, an [#permalink]

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11 Apr 2018, 23:46
EgmatQuantExpert wrote:
Learn structured approach to identify permutation and combination question - Exercise Question #1

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.

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

7C5 * 6C4 * 3C1 * 3C1 = 7!/(2!5!) * 6!/(2!4!) * 3!/(2!1!) * 3!/(2!1!) = 21*15*3*3 = 2835 --> D

imo, answer is option D.
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Re: In how many ways a cricket team consisting of 5 batsmen, 4 bowlers, an [#permalink]

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12 Apr 2018, 09:47
EgmatQuantExpert wrote:
Learn structured approach to identify permutation and combination question - Exercise Question #1

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.

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

Learn to use the Keyword Approach in Solving PnC question from the following article:

Article-1: Learn when to “Add” and “Multiply” in Permutation & Combination questions

Article-2: Learn structured approach to identify Permutation & Combination questions

A simple PS question where one has to choose 5 batsman from 7 batsman, 4 bowlers out of 6 bowlers, 1 wicket keeper out of 3 wicket keepers and 1 all rounder from 3 allrounders. So according to combinations principles, the number of ways we can choose r items from n items is found out as nCr which equals to n!/((n-r)!*r!). So here the solution is , 7C5*6C4*3C1*3C1 = 2835 (D)
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Joined: 04 Jan 2015
Posts: 1001
Re: In how many ways a cricket team consisting of 5 batsmen, 4 bowlers, an [#permalink]

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17 Apr 2018, 09:01
Hey everyone,

The official solution to the question has been posted.

Regards,
Ashutosh
e-GMAT
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Re: In how many ways a cricket team consisting of 5 batsmen, 4 bowlers, an   [#permalink] 17 Apr 2018, 09:01
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# In how many ways a cricket team consisting of 5 batsmen, 4 bowlers, an

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