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In how many ways a cricket team consisting of 5 batsmen, 4 bowlers, an
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Updated on: 13 Aug 2018, 06:06

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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:

Re: In how many ways a cricket team consisting of 5 batsmen, 4 bowlers, an
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Updated on: 17 Apr 2018, 07:47

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= \(^7c_5\)*\(^6c_4\)*\(^3c_1\)*\(^3c_1\)

Re: In how many ways a cricket team consisting of 5 batsmen, 4 bowlers, an
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11 Apr 2018, 22:46

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.

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

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12 Apr 2018, 08:47

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:

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)

Re: In how many ways a cricket team consisting of 5 batsmen, 4 bowlers, an
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18 Sep 2018, 13:32

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EgmatQuantExpert wrote:

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

Take the task of creating a cricket team and break it into stages and then apply the Fundamental Counting Principle

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. So, be sure to learn it.

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Re: In how many ways a cricket team consisting of 5 batsmen, 4 bowlers, an &nbs
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18 Sep 2018, 13:32