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# A soccer team of 11 players is to be formed out of a pool of 23

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Director
Joined: 22 Feb 2018
Posts: 597
A soccer team of 11 players is to be formed out of a pool of 23  [#permalink]

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10 Feb 2020, 22:32
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2
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Difficulty:

35% (medium)

Question Stats:

76% (02:53) correct 24% (03:05) wrong based on 46 sessions

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A soccer team of 11 players is to be formed out of a pool of 23 available players. The team should consist of 3 strikers, 4 midfielders, 3 defenders and 1 goalkeeper. The pool of 23 players consists of 6 strikers, 7 midfielders, 7 defenders and 3 goalkeepers. If Bruce, who is a striker, and David, who is a midfielder, should be a part of the team, what is the number of possible ways in which the team can be formed?

A) 7000
B) 14000
C) 21000
D) 27000
E) 77500
Intern
Joined: 27 Jan 2020
Posts: 1
A soccer team of 11 players is to be formed out of a pool of 23  [#permalink]

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17 Feb 2020, 05:03
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This a combination question .
Out of the 3 strikers and 4 mid-fielders we are supposed to pick , we have Bruce and David so we have to pick 2 strikers and 3 mid-fielders out of 5 strikers and 6 mid-fielders respectively as two are fixed . And 3 defenders out of 7 and 1 goal keeper out of 3 .

we use basic combination .
5C2 * 6C3 * 7C3 * 3C1

So we get C. 21000 ways which is the official answer .
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Joined: 18 Aug 2017
Posts: 6036
Location: India
Concentration: Sustainability, Marketing
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Re: A soccer team of 11 players is to be formed out of a pool of 23  [#permalink]

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17 Feb 2020, 10:53
out of total 23 players ;
strikers from 6 ; Bruce is chosen ; we have 5c2 choices
midifilder from 4 ; David is chosen ; we have 6c3
defenders ; 7c3
Gk ; 3c1

5c2*6c3*7c3*3c1 ; 21000
IMO C

Raxit85 wrote:
A soccer team of 11 players is to be formed out of a pool of 23 available players. The team should consist of 3 strikers, 4 midfielders, 3 defenders and 1 goalkeeper. The pool of 23 players consists of 6 strikers, 7 midfielders, 7 defenders and 3 goalkeepers. If Bruce, who is a striker, and David, who is a midfielder, should be a part of the team, what is the number of possible ways in which the team can be formed?

A) 7000
B) 14000
C) 21000
D) 27000
E) 77500
Manager
Joined: 22 Sep 2018
Posts: 76
Re: A soccer team of 11 players is to be formed out of a pool of 23  [#permalink]

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19 Feb 2020, 00:24
1
As we have to select 11 members out of 23, and then it is given 2 members are compulsory , we have only 9 members to select from remaining people ,

Remaining team is 2(s) , 3(M), 3(D), 1(GK).

Total members available is 5(s), 6(M), 7(D), 3(GK).

5C2 * 6C3 * 7C3 * 3C1 = 21000

SO OPTION C
Re: A soccer team of 11 players is to be formed out of a pool of 23   [#permalink] 19 Feb 2020, 00:24
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