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A folk group wants to have one concert on each of the seven consecutiv

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A folk group wants to have one concert on each of the seven consecutiv [#permalink]

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New post 12 Oct 2017, 11:08
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Question Stats:

58% (02:12) correct 42% (01:57) wrong based on 38 sessions

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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 is to be held in each of cities A, B, C, D and E. Two concerts are to be held in city F, but not on consecutive nights. In how many ways can the group decide on the venues for these seven concerts?

(A) 10 x 5!
(B) 14 x 5!
(C) 15 x 5!
(D) 20 x 5!
(E) 21 x 5!
[Reveal] Spoiler: OA

Last edited by fabiobf on 12 Oct 2017, 13:24, edited 1 time in total.

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Re: A folk group wants to have one concert on each of the seven consecutiv [#permalink]

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New post 12 Oct 2017, 11:27
fabiobf wrote:
A folk group wants to have one concert on each of the seven consecutive nights starting January 1 of next year. One concert is to be held in each of cities A, B, C, D and E. Two concerts are to be held in city F, but not on consecutive nights. In how many ways can the group decide on the venues for these seven concerts?

(A) 10 x 5!
(B) 14 x 5!
(C) 15 x 5!
(D) 20 x 5!
(E) 21 x 5!


Hi fabiobf,

Kindly follow the rules before posting questions.
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Re: A folk group wants to have one concert on each of the seven consecutiv [#permalink]

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New post 12 Oct 2017, 11:51
I came up with C - 15*5!

First, i wanted to find out how many ways city F could be placed in 2 days in 7 with no consecutive days. There is a pattern where the if you choose day 1 for F, there are 5 other days, if you choose day 2 for F, there are 4 other days, then 3 choices if start day 3, 2 choices starting day 4 and one option left if starting on day 5. These are "or" options, so add them together (5+4+3+2+1) = 15. Then there are 5 more days to fill with 5 cities which is 5*4*3*2*1 or 5!. When you combine F with the other cities, you need to multiply, so 15*5!: Choice C

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Re: A folk group wants to have one concert on each of the seven consecutiv [#permalink]

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New post 13 Oct 2017, 01:21
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fabiobf wrote:
A folk group wants to have one concert on each of the seven consecutive nights starting January 1 of next year. One concert is to be held in each of cities A, B, C, D and E. Two concerts are to be held in city F, but not on consecutive nights. In how many ways can the group decide on the venues for these seven concerts?

(A) 10 x 5!
(B) 14 x 5!
(C) 15 x 5!
(D) 20 x 5!
(E) 21 x 5!


The folk group can have the concerts in the following ways

_A_B_C_D_E_

City F can take any of 6 places as two concerts can't be held on consecutive nights.
Since there are 6 spots where the concerts can take place in City F,
we have 6c2 or 15 different ways of arranging these concerts.

Also, the concerts in the other 5 cities(A,B,C,D and E) can be arranged in 5! ways

Hence, the total number of ways in which the folk group can decide on its venues for each
of the seven concerts is 15*5!(Option C)
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Re: A folk group wants to have one concert on each of the seven consecutiv [#permalink]

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New post 13 Oct 2017, 02:31
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Hi,

Total ways of arranging = 7!
If we keep the the shows in city F together = 6!*2
Hence, when shows kept apart = 7! - (6!*2)

Can someone please explain the fault in this approach?

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Re: A folk group wants to have one concert on each of the seven consecutiv [#permalink]

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New post 13 Oct 2017, 03:23
Hey Avin, since a city is being repeated, the total ways ways of arranging will be 7!/2. And subtracting 6! From that gives the answer

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Re: A folk group wants to have one concert on each of the seven consecutiv   [#permalink] 13 Oct 2017, 03:23
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