Last visit was: 21 Nov 2024, 19:06 It is currently 21 Nov 2024, 19:06
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

GRE Prep 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 GRE 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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
PREVIOUS TOPIC
NEXT TOPIC

A play has two roles for men and four roles for women. If five men and

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30003
Own Kudos [?]: 36341 [1]
Given Kudos: 25927
Send PM
A play has two roles for men and four roles for women. If five men and [#permalink] New post   06 Apr 2022, 02:00
Expert Reply
1
Bookmarks
00:00

Question Stats:

75% (01:05) correct 25% (03:47) wrong based on 4 sessions

Hide Show timer Statistics

A play has two roles for men and four roles for women. If five men and 12 women try out for these parts, in how many different ways can the director choose people for the roles?

Show: ::
237,600



avatar
B
volcanictempest78
Intern
Intern
Joined: 03 Feb 2022
Posts: 46
Own Kudos [?]: 15 [0]
Given Kudos: 59
Send PM
Re: A play has two roles for men and four roles for women. If five men and [#permalink] New post   06 Apr 2022, 09:39
Kindly explain shouldn't the answer be 5c2 * 12c4 = 4950
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30003
Own Kudos [?]: 36341 [1]
Given Kudos: 25927
Send PM
Re: A play has two roles for men and four roles for women. If five men and [#permalink] New post   06 Apr 2022, 09:48
1
Expert Reply
The first male role can be filled by any of the five men, and the second by any of the remaining 4, for a total of 5 * 4 = 20 choices. Similarly, there are 12 options for the first female role, 11 for the next, 10 for the third, and 9 for the last. The total number of possibilities is thus 5 * 4 * 12 * 11 * 10 * 9 = 237,600.
avatar
B
volcanictempest78
Intern
Intern
Joined: 03 Feb 2022
Posts: 46
Own Kudos [?]: 15 [0]
Given Kudos: 59
Send PM
Re: A play has two roles for men and four roles for women. If five men and [#permalink] New post   06 Apr 2022, 10:00
Carcass wrote:
The first male role can be filled by any of the five men, and the second by any of the remaining 4, for a total of 5 * 4 = 20 choices. Similarly, there are 12 options for the first female role, 11 for the next, 10 for the third, and 9 for the last. The total number of possibilities is thus 5 * 4 * 12 * 11 * 10 * 9 = 237,600.


I get this answer when I account for arrangement in 5c2* 2! * 12c4 *4!
but this is not asking for arrangement, question mentions how director can chose among the 5 men for the two roles..in addition to this since it is not mentioned the roles are distinct won't we be double counting
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30003
Own Kudos [?]: 36341 [0]
Given Kudos: 25927
Send PM
Re: A play has two roles for men and four roles for women. If five men and [#permalink] New post   06 Apr 2022, 11:31
Expert Reply
volcanictempest78 wrote:
Carcass wrote:
The first male role can be filled by any of the five men, and the second by any of the remaining 4, for a total of 5 * 4 = 20 choices. Similarly, there are 12 options for the first female role, 11 for the next, 10 for the third, and 9 for the last. The total number of possibilities is thus 5 * 4 * 12 * 11 * 10 * 9 = 237,600.


I get this answer when I account for arrangement in 5c2* 2! * 12c4 *4!
but this is not asking for arrangement, question mentions how director can chose among the 5 men for the two roles..in addition to this since it is not mentioned the roles are distinct won't we be double counting


Sir

the explanation above is a fundamental counting principle

You must choose five men and then four. you do not have any sort of constraint

The same for the women

Regards
User avatar
P
GreenlightTestPrep
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12196 [1]
Given Kudos: 136
Send PM

Top Member of the Month
Re: A play has two roles for men and four roles for women. If five men and [#permalink] New post   06 Apr 2022, 12:09
1
volcanictempest78 wrote:
Carcass wrote:
The first male role can be filled by any of the five men, and the second by any of the remaining 4, for a total of 5 * 4 = 20 choices. Similarly, there are 12 options for the first female role, 11 for the next, 10 for the third, and 9 for the last. The total number of possibilities is thus 5 * 4 * 12 * 11 * 10 * 9 = 237,600.


I get this answer when I account for arrangement in 5c2* 2! * 12c4 *4!
but this is not asking for arrangement, question mentions how director can chose among the 5 men for the two roles..in addition to this since it is not mentioned the roles are distinct won't we be double counting


I agree. The author could have added a few extra words to inform us that the 6 roles are distinct/different.
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30003
Own Kudos [?]: 36341 [0]
Given Kudos: 25927
Send PM
Re: A play has two roles for men and four roles for women. If five men and [#permalink] New post   06 Apr 2022, 13:25
Expert Reply
For me, there is not so much room for misinterpretation...................
avatar
B
mehrdadvlc
Intern
Intern
Joined: 24 Oct 2021
Posts: 14
Own Kudos [?]: 10 [0]
Given Kudos: 17
Send PM
Re: A play has two roles for men and four roles for women. If five men and [#permalink] New post   06 Apr 2022, 23:55
Carcass wrote:
The first male role can be filled by any of the five men, and the second by any of the remaining 4, for a total of 5 * 4 = 20 choices. Similarly, there are 12 options for the first female role, 11 for the next, 10 for the third, and 9 for the last. The total number of possibilities is thus 5 * 4 * 12 * 11 * 10 * 9 = 237,600.

Would you please enlighten me why it is not 5*4 + 12*11*10*9 ?
Aren't men and female roles are two separate entities?
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30003
Own Kudos [?]: 36341 [1]
Given Kudos: 25927
Send PM
Re: A play has two roles for men and four roles for women. If five men and [#permalink] New post   07 Apr 2022, 02:58
1
Expert Reply
A play has two roles for men and four roles for women

and = multiplication
Prep Club for GRE Bot
gmatclubot
Re: A play has two roles for men and four roles for women. If five men and [#permalink]
07 Apr 2022, 02:58
Moderators:
adewale223
GRE Instructor
84 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1111 posts
VibhuAnurag
GRE Instructor
234 posts

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

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact