Permutation and combination

Question

there are 5 teachers , 4 girls students ,6 boys students . 5 teachers are required to sit in the first row ,4 girls students are required to sit in the second row , 6 boys students are requires to sit in the last row . In how many ways the sitting arrangement can be made ??

Anurag@Gurome · Answer

abcd1111 wrote:there are 5 teachers , 4 girls students ,6 boys students . 5 teachers are required to sit in the first row ,4 girls students are required to sit in the second row , 6 boys students are requires to sit in the last row . In how many ways the sitting arrangement can be made ??

5 teachers can be arranged among themselves in 5! = 120 ways
4 girls can be arranged among themselves in 4! = 24 ways
6 boys can be arranged among themselves in 6! = 720 ways

Hence, total number of seating arrangements = 120*24*720

abcd1111 · Answer

Hi Anurag@Gurome thanks a lot for your explanation .

heymayank08 · Answer

Anurag@Gurome wrote:abcd1111 wrote: Hence, total number of seating arrangements = 120*24*720 hi anurag, don't u think that this will be for the arrangement in which we have to arrange among teachers, boys adn girls, shouldn't the answer be : 5!.4!.6!.(3) *3 because their rows need to be arranged. please correct me if i am wrong.

heymayank08 · Answer

Anurag@Gurome wrote:abcd1111 wrote: Hence, total number of seating arrangements = 120*24*720 hi anurag, don't u think that this will be for the arrangement in which we have to arrange among teachers, boys adn girls, shouldn't the answer be : 5!.4!.6!.(3) *3 because their rows need to be arranged. please correct me if i am wrong.

sandeep_thaparianz · Answer

heymayank08 wrote:Anurag@Gurome wrote:abcd1111 wrote: Hence, total number of seating arrangements = 120*24*720 hi anurag, don't u think that this will be for the arrangement in which we have to arrange among teachers, boys adn girls, shouldn't the answer be : 5!.4!.6!.(3) *3 because their rows need to be arranged. please correct me if i am wrong. It is already mentioned in question the pattern in which they are to be seated row wise.. So Drop *3 multiplication

heymayank08 · Answer

sandeep_thaparianz wrote:heymayank08 wrote:Anurag@Gurome wrote:abcd1111 wrote: Hence, total number of seating arrangements = 120*24*720 hi anurag, don't u think that this will be for the arrangement in which we have to arrange among teachers, boys adn girls, shouldn't the answer be : 5!.4!.6!.(3) *3 because their rows need to be arranged. please correct me if i am wrong. It is already mentioned in question the pattern in which they are to be seated row wise.. So Drop *3 multiplication yeah thts wat i am saying.. since they are to be sated in 3 rows so the rows in thmselves can be arranged!

Anurag@Gurome · Answer

heymayank08 wrote:hi anurag,
don't u think that this will be for the arrangement in which we have to arrange among teachers, boys adn girls,
shouldn't the answer be :
5!.4!.6!.(3)

*3 because their rows need to be arranged.
please correct me if i am wrong.

Read the question carefully.
The question says "5 teachers are required to sit in the first row ,4 girls students are required to sit in the second row , 6 boys students are requires to sit in the last row"

This means we cannot rearrange the rows.
The teachers will always seat in the first row, the girls in the second row and the boys in the third.

Hope that helps.

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/

Choose how you want to prepare

Get Ready for GMAT Test Day Faster with Live Online Classes

Target Test Prep EA OnDemand

Target Test Prep GMAT OnDemand

Permutation and combination

GMAT/MBA Expert

GMAT/MBA Expert

Chicago Booth

GMAT Course Reviews

Admissions Consulting Reviews

FREE GMAT PREP RESOURCES

GMAT PREP DEAL TRACKER