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From a group of 10 boys and 7 girls, how many different 6-person hocke

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From a group of 10 boys and 7 girls, how many different 6-person hocke [#permalink]

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New post 13 May 2017, 14:33
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From a group of 10 boys and 7 girls, how many different 6-person hockey teams can be formed if the team must consist of 3 girls and 3 boys?

A. 155
B. 1200
C. 1360
D. 4200
E. 12376

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Re: From a group of 10 boys and 7 girls, how many different 6-person hocke [#permalink]

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New post 13 May 2017, 20:36
Bunuel wrote:
From a group of 10 boys and 7 girls, how many different 6-person hockey teams can be formed if the team must consist of 3 girls and 3 boys?

A. 155
B. 1200
C. 1360
D. 4200
E. 12376


Select 3 girls from 7 girls, there are \(7C3= \frac{5\times 6 \times 7}{2 \times 3}=35\) different selections.

Select 3 boys from 10 boys, there are \(10C3=\frac{8 \times 9 \times 10}{2 \times 3}=120\) different selections

The total combination is \(35 \times 120 =4200\)

The answer is D.
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Re: From a group of 10 boys and 7 girls, how many different 6-person hocke [#permalink]

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New post 13 May 2017, 20:55
Bunuel wrote:
From a group of 10 boys and 7 girls, how many different 6-person hockey teams can be formed if the team must consist of 3 girls and 3 boys?

A. 155
B. 1200
C. 1360
D. 4200
E. 12376


Step 1: SELECT 3 boys out of 10 available boys = 10C3 = 120

Step 2: SELECT 3 Girls out of 7 available Girls = 7C3 = 35


For dependent events, we multiply the steps

Total Ways to make team = 10C3 * 7C3 = 120*35 = 4200

Answer: Option D
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Re: From a group of 10 boys and 7 girls, how many different 6-person hocke [#permalink]

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New post 14 May 2017, 15:14
The solution is numbers of chosen boys times the number of chosen girls, therefore:

\(10C3 * 7C3 = \frac{10*9*8}{1*2*3} * \frac{7*6*5}{1*2*3}= 120*35=4200\)

The Correct option is: D
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Re: From a group of 10 boys and 7 girls, how many different 6-person hocke [#permalink]

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New post 18 May 2017, 20:09
1
Bunuel wrote:
From a group of 10 boys and 7 girls, how many different 6-person hockey teams can be formed if the team must consist of 3 girls and 3 boys?

A. 155
B. 1200
C. 1360
D. 4200
E. 12376


We need to determine how many 6-person hockey teams can be formed if the team must consist of 3 girls and 3 boys.

The number of ways to select the boys is 10C3 = 10!/[3!(10-3)!] = (10 x 9 x 8)/3! = (10 x 9 x 8)/(3 x 2) = 120.

The number of ways to select the girls is 7C3 = 7!/[3!(7-3)!] = (7 x 6 x 5)/(3 x 2) = 35.

Thus, the number of ways to select the teams is 120 x 35 = 4,200.

Answer: D
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Re: From a group of 10 boys and 7 girls, how many different 6-person hocke   [#permalink] 18 May 2017, 20:09
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