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.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

4 married couple have bought 8 seats in a raw for a football [#permalink]
20 Jul 2004, 08:24

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct
0% (00:00) wrong based on 0 sessions

4 married couple have bought 8 seats in a raw for a football game.

b) In how many ways can they be seated if each couple is not to sit together with the husband to the left of his wife?
c) In how many ways can they be seated if each couple is not to sit together?
d) In how many ways can they be seated if all men are to sit together?
e) In how many ways can they be seated if none of the men are to sit together and none of the women are sit together?

b) In how many ways can they be seated if each couple is not to sit together with the husband to the left of his wife?

total number of ways 4 couples can sit is 8!
number of ways couples can sit together with husbands sitting to the left of wife : since the wife husband cant be split and have to sit together it is 4! ways

whwhwhwh

so ans to b is 8! - 4!

C) similarly couples can sit together in 4!*2 ways
(whwhwhwh and hwhwhwhw)

so the ans is 8! - 4!*2 ways

the rest of the answers remain the same
D) 5!*4! = 2280
E) 2*4!*4! = 1152

Boksana, just saw Ur answers, but still thot of posting my answers... btw, any explanation for your answers? Ur answers seems too so small numbers though for a 8!...

b) In how many ways can they be seated if each couple is not to sit together with the husband to the left of his wife?
Total number of ways they can be seated = 8! Number of ways they can be seated - with each couple sitting together w/ h left to w = 4! (within a couple of HW is fixed and need not be played with) So, ans for b = 8! - 4!

c) In how many ways can they be seated if each couple is not to sit together?
Total number of ways they can be seated = 8! Number of ways they can be seated - with each couple sitting together = 4!*2! (within a couple of HW and WH can be played with) So, ans for c = 8! - 4!*2!

d) In how many ways can they be seated if all men are to sit together?
Number of entities to seat = 5, hence ways = 5! Number of ways men can be seated among themselves = 4! SO, anc for d = 5!*4!

e) In how many ways can they be seated if none of the men are to sit together and none of the women are sit together?
Total number of ways they can be seated = 8! Number of ways they can be seated - men sitting together and women sitting together = 2!*4!*4! (first 2! for two entities, the two 4! are for men and women to reorder within themselves) So, ans for d = 8! - 2!*4!*4!

[quote="hardworker_indian"]Boksana, just saw Ur answers, but still thot of posting my answers... btw, any explanation for your answers? Ur answers seems too so small numbers though for a 8!...

e) In how many ways can they be seated if none of the men are to sit together and none of the women are sit together?
[color=blue]Total number of ways they can be seated = 8!
Number of ways they can be seated - men sitting together and women sitting together = 2!*4!*4! (first 2! for two entities, the two 4! are for men and women to reorder within themselves)
So, ans for d = 8! - 2!*4!*4![/color][/quote]ct

hi hardworker_indian,

I'm not sure why u want to subtract 2!*4!*4! from 8!. remember that will give you all possible combinations where husband wife are together
whwhwhwh etc etc where as what we are looking for is wwww hhhh type of combinations (you have to imagine that there are spectators sitting in between them) and so the ans I think is 2!*4!*4!

What I found was wrong; my formula was
Number of ways, none of the H sit together and none of W sit together
=
total number of ways -
number of ways that H sit together and W sit together (HHHHWWWW and WWWWHHHH)
=
8! -
2!*4!*4!

The loophole was that this includes other cases like three H sitting together, which is not desired... (Eg: HHHWWWWH)

*PHEW*. Do you sometimes have that feeling where you try and cram as much as is humanly possible in the 24 hours that constitute a day and that time...

Ah yes. Funemployment. The time between when you quit your job and when you start your MBA. The promised land that many MBA applicants seek. The break that every...

It is that time of year again – time for Clear Admit’s annual Best of Blogging voting. Dating way back to the 2004-2005 application season, the Best of Blogging...