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# In how many ways can the team of 3 boys and 3 girls be formed out of 7

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CEO
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In how many ways can the team of 3 boys and 3 girls be formed out of 7  [#permalink]

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27 Jan 2019, 22:55
00:00

Difficulty:

55% (hard)

Question Stats:

35% (01:46) correct 65% (02:40) wrong based on 31 sessions

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In how many ways can the team of 3 boys and 3 girls be formed out of 7 boys and 5 girls if one particular boy and one particular girl can not be together in the team?

A) 926
B) 350
C) 340
D) 260
E) 200

Source: http://www.GMATinsight.com

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Re: In how many ways can the team of 3 boys and 3 girls be formed out of 7  [#permalink]

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27 Jan 2019, 23:18
GMATinsight wrote:
In how many ways can the team of 3 boys and 3 girls be formed out of 7 boys and 5 girls if one particular boy and one particular girl can not be together in the team?

A) 926
B) 350
C) 340
D) 260
E) 200

Source: http://www.GMATinsight.com

IMO D

Total number of ways 3 boys and 3 girls be formed out of 7 boys and 5 girls, when no condition is placed
= 7C3 * 5C3
= 350 ways

Answer now cannot be A and B. since we will be subtracting those cases when they(one particular boy and one particular girl ) are included in the team
if they take 1 position each in the 3 member team
Boys team will become 1* 6C2 = 15 ways
Girls team will become 1*4C2 = 6 ways

Total number of ways = 90 ways

In how many ways can the team of 3 boys and 3 girls be formed out of 7 boys and 5 girls if one particular boy and one particular girl can not be together in the team
= 350 - 90
= 260 ways
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Re: In how many ways can the team of 3 boys and 3 girls be formed out of 7  [#permalink]

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28 Jan 2019, 00:44
total ways to make a team : 7c3*5c3 = 35*10 = 350

now since we dont want 1 specific boy & 1 girl not to be part of team ; we can consider a case where in they both are included in the team.

so for boy : 6c2 *1 ; 15
girl : 4c2*1 ; 6

15*6 = 90 ways

so total no of ways in which 1 specific boy & 1 girl not to be part of team ; total ways - both in team ; 350-90 = 260
IMO D

GMATinsight wrote:
In how many ways can the team of 3 boys and 3 girls be formed out of 7 boys and 5 girls if one particular boy and one particular girl can not be together in the team?

A) 926
B) 350
C) 340
D) 260
E) 200

Source: http://www.GMATinsight.com

_________________

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Intern
Joined: 30 May 2017
Posts: 16
Re: In how many ways can the team of 3 boys and 3 girls be formed out of 7  [#permalink]

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28 Jan 2019, 03:10
the other way of calculating the number of arrangements would be to calculate the number of arrangements for each of the scenarios.

1- The Boy and the girl are not selected

3C6*3C4 = 80

2 - The boy is selcted but the girl isn't

2C6*3C4 = 60

3- The girl was selected and the boy wasn't

3C6*2C4 = 120

CEO
Status: GMATINSIGHT Tutor
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Posts: 2788
Location: India
GMAT: INSIGHT
Schools: Darden '21
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Re: In how many ways can the team of 3 boys and 3 girls be formed out of 7  [#permalink]

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28 Jan 2019, 05:27
GMATinsight wrote:
In how many ways can the team of 3 boys and 3 girls be formed out of 7 boys and 5 girls if one particular boy and one particular girl can not be together in the team?

A) 926
B) 350
C) 340
D) 260
E) 200

Source: http://www.GMATinsight.com

Let, Boys are A B C D E F G and Girls are P Q R S T

and A and P can NOT be together

Method-1:

Favourable cases = Total ways of making team of 3 boys and 3 girls - Ways of making team of 3 boys and 3 girls such that A and P are together

i.e. Favourable teams = 7C3*5C3 - 6C2*4C2 = 35*10 - 15*6 = 350 - 90 = 260

Method-2:
A is NOT selected and P is selected - 6C3*4C2 = 20*5 = 120
P is NOT selected and A is selected - 6C2*4C3 = 15*4 = 60
A and P both are NOT selected - 6C3*4C3 = 20*4 = 80

Total ways = 120+60+80 = 260

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Re: In how many ways can the team of 3 boys and 3 girls be formed out of 7   [#permalink] 28 Jan 2019, 05:27
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