GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 24 Aug 2019, 13:19

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
B
Joined: 11 Nov 2013
Posts: 27
There are 10 male and 8 female dancers in a club.  [#permalink]

Show Tags

New post 05 Aug 2019, 06:52
7
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

22% (01:46) correct 78% (01:56) wrong based on 51 sessions

HideShow timer Statistics

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
Intern
User avatar
B
Joined: 20 Feb 2018
Posts: 36
Location: India
Schools: ISB '20, IIMA PGPX"20
GMAT 1: 610 Q47 V28
GPA: 3.8
CAT Tests
Re: There are 10 male and 8 female dancers in a club.  [#permalink]

Show Tags

New post 05 Aug 2019, 07:40
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
Intern
avatar
B
Joined: 11 Nov 2013
Posts: 27
Re: There are 10 male and 8 female dancers in a club.  [#permalink]

Show Tags

New post 06 Aug 2019, 04:23
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
Intern
avatar
B
Joined: 26 Mar 2018
Posts: 2
Location: India
GMAT 1: 710 Q50 V36
GPA: 3.07
There are 10 male and 8 female dancers in a club.  [#permalink]

Show Tags

New post 06 Aug 2019, 04:45
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
Intern
User avatar
B
Joined: 20 Feb 2018
Posts: 36
Location: India
Schools: ISB '20, IIMA PGPX"20
GMAT 1: 610 Q47 V28
GPA: 3.8
CAT Tests
Re: There are 10 male and 8 female dancers in a club.  [#permalink]

Show Tags

New post 06 Aug 2019, 07:48
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
Senior Manager
Senior Manager
avatar
G
Joined: 30 Sep 2017
Posts: 250
Concentration: Technology, Entrepreneurship
GMAT 1: 720 Q49 V40
GPA: 3.8
WE: Engineering (Real Estate)
There are 10 male and 8 female dancers in a club.  [#permalink]

Show Tags

New post 06 Aug 2019, 10:10
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.

Answer is (D)

Hit +1 kudo for this explanation

Posted from my mobile device
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 7467
Location: United States (CA)
Re: There are 10 male and 8 female dancers in a club.  [#permalink]

Show Tags

New post 11 Aug 2019, 19:50
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.

Answer: D
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: There are 10 male and 8 female dancers in a club.   [#permalink] 11 Aug 2019, 19:50
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne