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A group of four women and three men have tickets for seven a [#permalink]
30 Dec 2009, 20:43
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A
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C
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Difficulty:
55% (hard)
Question Stats:
62% (01:59) correct
38% (01:24) wrong based on 290 sessions
A group of four women and three men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?
Re: Combinations Problem -- Arrangement of Seats [#permalink]
30 Dec 2009, 23:31
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This post received KUDOS
IMO C
7 people can be seated in 7! ways
take 3 men as one unit ----> tot 5 people can be seated in 5 ways *(no. of ways in which 4 women can be seated amng themselves ) * ( no. of ways in which 3 men cen be seated amng themselves)=5*4!*3!=5!*3!
tot no. of ways in which 3 men are not seated in adjacent seats=tot arrangements - 5!*3!=7!-5!*3! _________________
GMAT is not a game for losers , and the moment u decide to appear for it u are no more a loser........ITS A BRAIN GAME
Re: Combinations Problem -- Arrangement of Seats [#permalink]
31 Dec 2009, 02:35
xcusemeplz2009 wrote:
IMO C
7 people can be seated in 7! ways
take 3 men as one unit ----> tot 5 people can be seated in 5 ways *(no. of ways in which 4 women can be seated amng themselves ) * ( no. of ways in which 3 men cen be seated amng themselves)=5*4!*3!=5!*3!
tot no. of ways in which 3 men are not seated in adjacent seats=tot arrangements - 5!*3!=7!-5!*3!
I understand having 7! total arrangements and subtracting out 4!3!, but why do why multiply this term we subtract out, 4!3! by 5? Is it because there are 5 situations where 3 men are next to each other (see below)?
Re: Combinations Problem -- Arrangement of Seats [#permalink]
31 Dec 2009, 18:53
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This post received KUDOS
Expert's post
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A group of four women and three men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?
There are 3 men and 4 women, we want to calculate the seating arrangements if three men do not sit together, like MMM.
Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 7 persons without restriction. Thus we'll get the # of arrangements asked in the question.
1. Total # of arrangements of 7 is 7!.
2. # of arrangements when 3 men are seated together, like MMM;
Among themselves these 3 men can sit in 3! # of ways, Now consider these 3 men as one unit like this {MMM}. We'll have total of 5 units: {MMM}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!.
Hence total # of arrangements when 3 men sit together is: 3!5!.
# of arrangements when 3 men do not sit together would be: 7!-3!5!.
Re: Combinations Problem -- Arrangement of Seats [#permalink]
01 Jan 2010, 09:07
C is the answer!
Total arrangments posb = 7!
Treat 3 Men as a single unit. Hence Men + 4 women can be arranged in 5 ways. 3 Men within the single unit can be arranged in 3! ways 4 women can be arranged in 4! ways.
Therefore no of posb when 3 men sit adjacent to each other (as a single unit) = 5x3!x4! = 5! x 3!
Hence no of posb when 3 men dont sit together = 7! - 5! x 3!
Cheers! JT _________________
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Re: A group of four women and three men have tickets for seven a [#permalink]
21 Sep 2013, 11:40
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Re: Combinations Problem -- Arrangement of Seats [#permalink]
21 Sep 2013, 11:46
1
This post received KUDOS
Bunuel wrote:
A group of four women and three men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?
There are 3 men and 4 women, we want to calculate the seating arrangements if three men do not sit together, like MMM.
Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 7 persons without restriction. Thus we'll get the # of arrangements asked in the question.
1. Total # of arrangements of 7 is 7!.
2. # of arrangements when 3 men are seated together, like MMM;
Among themselves these 3 men can sit in 3! # of ways, Now consider these 3 men as one unit like this {MMM}. We'll have total of 5 units: {MMM}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!.
Hence total # of arrangements when 3 men sit together is: 3!5!.
# of arrangements when 3 men do not sit together would be: 7!-3!5!.
Answer: C.
Hope it's clear.
Just wanted to share this little thing Bunuel.
You tend to write "Hope it's clear." after every solution, but there "never is" a chance that you have explained something and it isn't clear. Unlimited Kudos to you, and RESPECT! _________________
Re: A group of four women and three men have tickets for seven a [#permalink]
29 Dec 2013, 16:18
R2I4D wrote:
A group of four women and three men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?
Re: Combinations Problem -- Arrangement of Seats [#permalink]
11 Jun 2014, 20:52
Bunuel wrote:
A group of four women and three men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?
There are 3 men and 4 women, we want to calculate the seating arrangements if three men do not sit together, like MMM.
Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 7 persons without restriction. Thus we'll get the # of arrangements asked in the question.
1. Total # of arrangements of 7 is 7!.
2. # of arrangements when 3 men are seated together, like MMM;
Among themselves these 3 men can sit in 3! # of ways, Now consider these 3 men as one unit like this {MMM}. We'll have total of 5 units: {MMM}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!.
Hence total # of arrangements when 3 men sit together is: 3!5!.
# of arrangements when 3 men do not sit together would be: 7!-3!5!.
Answer: C.
Hope it's clear.
A silly doubt that have cropped up all of a sudden
Bunuel, I've a doubt. Why are we not dividing 5! by 4! as there are 4 of the same type in the group. I know I'm wrong. Kindly help me where
Re: Combinations Problem -- Arrangement of Seats [#permalink]
12 Jun 2014, 03:53
Expert's post
sgangs wrote:
Bunuel wrote:
A group of four women and three men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?
There are 3 men and 4 women, we want to calculate the seating arrangements if three men do not sit together, like MMM.
Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 7 persons without restriction. Thus we'll get the # of arrangements asked in the question.
1. Total # of arrangements of 7 is 7!.
2. # of arrangements when 3 men are seated together, like MMM;
Among themselves these 3 men can sit in 3! # of ways, Now consider these 3 men as one unit like this {MMM}. We'll have total of 5 units: {MMM}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!.
Hence total # of arrangements when 3 men sit together is: 3!5!.
# of arrangements when 3 men do not sit together would be: 7!-3!5!.
Answer: C.
Hope it's clear.
A silly doubt that have cropped up all of a sudden
Bunuel, I've a doubt. Why are we not dividing 5! by 4! as there are 4 of the same type in the group. I know I'm wrong. Kindly help me where
All men and women are different, so no need for factorial correction there. For example, arrangement {Bill, Bob, Ben} {Ann}, {Beth}, {Carol}, {Diana} is different from {Bill, Bob, Ben}, {Beth}, {Carol}, {Diana}, {Ann}.
Re: A group of four women and three men have tickets for seven a [#permalink]
28 Jul 2015, 19:16
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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