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# There are 10 male and 8 female dancers in a club.

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Intern
Joined: 11 Nov 2013
Posts: 26
There are 10 male and 8 female dancers in a club.  [#permalink]

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05 Aug 2019, 05:52
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Difficulty:

95% (hard)

Question Stats:

21% (01:46) correct 79% (01:54) wrong based on 53 sessions

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There are 10 male and 8 female dancers in a club. If the club is to form two groups, each having 1 male and 1 female dancer, in how many ways can it be done?

(A)143
(B) 160
(C) 1,260
(D) 2,520
(E) 5,040
Intern
Joined: 20 Feb 2018
Posts: 33
Location: India
Schools: ISB '20, IIMA PGPX"20
GMAT 1: 610 Q47 V28
GPA: 3.8
Re: There are 10 male and 8 female dancers in a club.  [#permalink]

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05 Aug 2019, 06:40
2
first group can be created in 10M*8F =80 ways
second group can be created in remaining 9M*7F=63 ways

so total no. of ways 80*63=5040
but there will be times when the choices in first group will be similar to choices in second group so divide it by 2!

hence 2520

IMO D
Intern
Joined: 11 Nov 2013
Posts: 26
Re: There are 10 male and 8 female dancers in a club.  [#permalink]

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06 Aug 2019, 03:23
1
lifeforhuskar wrote:
first group can be created in 10M*8F =80 ways
second group can be created in remaining 9M*7F=63 ways

so total no. of ways 80*63=5040
but there will be times when the choices in first group will be similar to choices in second group so divide it by 2!

hence 2520

IMO D

I did not get 'but there will be times when the choices in first group will be similar to choices in second group so divide it by 2!'?
Intern
Joined: 26 Mar 2018
Posts: 11
Location: India
GPA: 4
There are 10 male and 8 female dancers in a club.  [#permalink]

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06 Aug 2019, 03:45
lifeforhuskar wrote:
first group can be created in 10M*8F =80 ways
second group can be created in remaining 9M*7F=63 ways

so total no. of ways 80*63=5040
but there will be times when the choices in first group will be similar to choices in second group so divide it by 2!

hence 2520

IMO D

How there will be times when both the groups will have similar choices?

Aren't we taking care of that when we consider 10 and 8 for first group and 9 and 7 for second?

Posted from my mobile device
Intern
Joined: 20 Feb 2018
Posts: 33
Location: India
Schools: ISB '20, IIMA PGPX"20
GMAT 1: 610 Q47 V28
GPA: 3.8
Re: There are 10 male and 8 female dancers in a club.  [#permalink]

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06 Aug 2019, 06:48
3
jack0997 wrote:
lifeforhuskar wrote:
first group can be created in 10M*8F =80 ways
second group can be created in remaining 9M*7F=63 ways

so total no. of ways 80*63=5040
but there will be times when the choices in first group will be similar to choices in second group so divide it by 2!

hence 2520

IMO D

I did not get 'but there will be times when the choices in first group will be similar to choices in second group so divide it by 2!'?

Think of it like this:
abcdefghij 10 males
klmnopqr 8 females

lets say we create first group
ak --group 1
and second group
bl --group 2
so this is out of 5040 , 1 way of selecting 2 group

second way will be
bl--group1
ak--group2
this will be again 1 ways of selecting 2 group in 5040

but as we have already taken this combination, we should divide the whole set 5040 by 2 to get the correct ways

Hope it helps
Kudos if you like
Director
Joined: 30 Sep 2017
Posts: 928
GMAT 1: 720 Q49 V40
GPA: 3.8
There are 10 male and 8 female dancers in a club.  [#permalink]

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06 Aug 2019, 09:10
1
Group 1 can be formed in 10*8=80 ways.
Group 2 can be formed in 9*7=63 ways.

If we differentiate the sequence strictly, total no. of ways can be 80*63=5,040. However, we should not consider such strict sequence, e.g. A+B in group 1 and C+D in group 2 sensically make no difference with C+D in group 1 and A+B. Therefore, 5,040 ways have to be divided by 2! groups = 2,520 ways.

Hit +1 kudo for this explanation

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Re: There are 10 male and 8 female dancers in a club.  [#permalink]

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11 Aug 2019, 18:50
jack0997 wrote:
There are 10 male and 8 female dancers in a club. If the club is to form two groups, each having 1 male and 1 female dancer, in how many ways can it be done?

(A)143
(B) 160
(C) 1,260
(D) 2,520
(E) 5,040

The number of ways to select the first group of 1 male and 1 female dancers is 10 x 8 = 80. The number of ways to select the next group is 9 x 7 = 63. Notice that when we multiply 80 and 63, we will have counted each pair of groups twice: If AB is one group and CD is another group; we first count AB as the first group and CD as the second group and then, we count CD as the first group and AB as the second group, but these pairs of groups actually represent one of the possibilities. Thus, we need to divide the product by 2. Therefore, the total number of ways to select the 2 groups is 80 x 63 x 1/2 = 2,520.

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Re: There are 10 male and 8 female dancers in a club.   [#permalink] 11 Aug 2019, 18:50