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A folk group wants to have one concert on each of the seven Updated on: 16 Apr 2008, 23:27
Originally posted by kevincan on 16 Apr 2008, 14:14.
Last edited by kevincan on 16 Apr 2008, 23:27, edited 1 time in total.
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A folk group wants to have one concert on each of the seven consecutive nights starting January 1 of next year. One concert will be held in each of cities A, B, C, D and E, and two will be held in city F , one on each of two non-consecutive nights. In how many ways can the group decide on the venues for these seven concerts?

Sorry, no choices! Let's see what we come up with...



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A folk group wants to have one concert on each of the seven 16 Apr 2008, 19:10
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kevincan
A folk group wants to have one concert on each of the seven consecutive nights starting January 1 of next year. One concert will be held in each of cities A, B, C, D and E, and two will be held in city F , one of each of two non-consecutive nights. In how many ways can the group decide on the venues for these seven concerts?

Sorry, no choices! Let's see what we come up with...
Show more

The wording is a bit confusing at the red part.
Here is my shot at it:
A, B, C, D, E, F, F => Total 8!
Can't have (F,F) together, and the total combination of that is:
A, B, C, D, E, (F, F) => Total 6!
Ans = 8! - 6!
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A folk group wants to have one concert on each of the seven 16 Apr 2008, 21:07
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kevincan
A folk group wants to have one concert on each of the seven consecutive nights starting January 1 of next year. One concert will be held in each of cities A, B, C, D and E, and two will be held in city F, one of each of two non-consecutive nights. In how many ways can the group decide on the venues for these seven concerts?

Sorry, no choices! Let's see what we come up with...

The wording is a bit confusing at the red part.
Here is my shot at it:
A, B, C, D, E, F, F => Total 8!
Can't have (F,F) together, and the total combination of that is:
A, B, C, D, E, (F, F) => Total 6!
Ans = 8! - 6!
Show more

Why you did 8! and 6! instead of 7! and 5!?

the red part means, imo, 2 concerts cannot be happen consecutively in city F. suppose if one concert held on 1 then next can be on either of 3 or 4 or 5 or 6 or 7 and so on.

so total possibilities = 7!
consecutive concerts in city F = 2 (5!)
so no of ways the concert can be held = 7!- 2 (5!)
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A folk group wants to have one concert on each of the seven 16 Apr 2008, 23:09
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is it \(6*6* 5!\)

There are 6 possible ways to arrange two consecutive concerts in a city and remaining 5 can be arranged in 5 cities 5! ways. Also we can pick city for double concert in 6 ways.
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A folk group wants to have one concert on each of the seven 17 Apr 2008, 06:27
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kevincan
A folk group wants to have one concert on each of the seven consecutive nights starting January 1 of next year. One concert will be held in each of cities A, B, C, D and E, and two will be held in city F, one of each of two non-consecutive nights. In how many ways can the group decide on the venues for these seven concerts?

Sorry, no choices! Let's see what we come up with...

The wording is a bit confusing at the red part.
Here is my shot at it:
A, B, C, D, E, F, F => Total 8!
Can't have (F,F) together, and the total combination of that is:
A, B, C, D, E, (F, F) => Total 6!
Ans = 8! - 6!

Why you did 8! and 6! instead of 7! and 5!?

the red part means, imo, 2 concerts cannot be happen consecutively in city F. suppose if one concert held on 1 then next can be on either of 3 or 4 or 5 or 6 or 7 and so on.

so total possibilities = 7!
consecutive concerts in city F = 2 (5!)
so no of ways the concert can be held = 7!- 2 (5!)
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Yea, it should be 7! for the total, I think I was dreaming.
I think it should be 7! - 6! though, two concerts in F doesn't differentiate which comes first.
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A folk group wants to have one concert on each of the seven 17 Apr 2008, 06:39
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So when are we to get OA and OE on this.

Looks like bkk* answer matches with what I have got with different way...want to make sure my approach is right.

7!-6!= 6!*(7-1) = 6!*6 = 6*6*5!
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A folk group wants to have one concert on each of the seven 17 Apr 2008, 22:44
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Step One: Decide which two non-consecutive concerts will be be held in F: 7C2 - 6 = 15
Step Two: Assign venues A, B, C, D and E to the remaining 5 concerts: 5! = 120

Answer: 15 x 120= 1800
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A folk group wants to have one concert on each of the seven 17 Apr 2008, 23:40
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Kevincan

I had 6*6*120

I see that I made a mistake assuming any of the cities is valid for double concert, for that I can reduce my answer to

6*120

I dont get your calculation on \(7C2-6\)
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A folk group wants to have one concert on each of the seven 18 Apr 2008, 18:24
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kevincan
Step One: Decide which two non-consecutive concerts will be be held in F: 7C2 - 6 = 15
Step Two: Assign venues A, B, C, D and E to the remaining 5 concerts: 5! = 120

Answer: 15 x 120= 1800
Show more

did not get what you did! :roll:
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A folk group wants to have one concert on each of the seven 18 Apr 2008, 22:54
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kevincan
Step One: Decide which two non-consecutive concerts will be be held in F: 7C2 - 6 = 15
Step Two: Assign venues A, B, C, D and E to the remaining 5 concerts: 5! = 120

Answer: 15 x 120= 1800
Show more

Clarifying Step One: Of the seven days, choose two on which a concert will be held in F. There are 7C2 =7!/5!2! ways of doing so, but we must eliminate the 6 ways in which two consecutive days are chosen
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A folk group wants to have one concert on each of the seven 18 Apr 2008, 23:18
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kevincan
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Step One: Decide which two non-consecutive concerts will be be held in F: 7C2 - 6 = 15
Step Two: Assign venues A, B, C, D and E to the remaining 5 concerts: 5! = 120

Answer: 15 x 120= 1800

Clarifying Step One: Of the seven days, choose two on which a concert will be held in F. There are 7C2 =7!/5!2! ways of doing so, but we must eliminate the 6 ways in which two consecutive days are chosen
Show more


Based on how I interpreted it , I thought whats required is opposite of above bold-underlined statemant you made....its 6ways we can choose a city as concert in city F has 2 back to back events.

Not sure what I am missing.
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A folk group wants to have one concert on each of the seven 19 Apr 2008, 06:53
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The question specifies that the two concerts in F must not be on consecutive nights
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A folk group wants to have one concert on each of the seven 19 Apr 2008, 08:07
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I am not good for GMAT. I cant even read question well. :cry:
No point knowing all the math behind if question is not read properly. Lesson learnt, again!

With this rather important correction :P I agree with your answer.
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A folk group wants to have one concert on each of the seven 22 Apr 2008, 04:25
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Here's my shot at it:

F 5 4 3 2 1 F= 120 ways
F 5 4 3 2 F 1= 120 ways *2 (Since it is symmetric to _ F _ _ _ _ F)
F 5 4 3 F 2 1 = 120 ways * 2 (symmetric to _ _ F _ __ F)

These are the nly ways, and I am gettinn the ans to be 600.

Does anyone have the OA/OE?
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A folk group wants to have one concert on each of the seven 22 Apr 2008, 08:10
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OA and OE

Quote:
Step One: Decide which two non-consecutive concerts will be be held in F: 7C2 - 6 = 15
Step Two: Assign venues A, B, C, D and E to the remaining 5 concerts: 5! = 120

Answer: 15 x 120= 1800
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