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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
A folk group wants to have one concert on each of the seven consecutiv
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27 Nov 2021, 04:24
27 Nov 2021, 04:24
Expert Reply
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Question Stats:
60% (02:10) correct
40% (03:32) wrong based on 5 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!
(A) 10 x 5!
(B) 14 x 5!
(C) 15 x 5!
(D) 20 x 5!
(E) 21 x 5!
Re: A folk group wants to have one concert on each of the seven consecutiv
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28 Nov 2021, 09:55
28 Nov 2021, 09:55
Expert Reply
Total ways = arranging A, B, C, D, E, F, F = 7!/2!
Calculate the number of ways that 2 shows in city F are done together
= take FF as a single bock
= [FF], A, B, C, D, E
= 6!*2!/2!
So, required number of ways = 7!/2! - 6!*2!/2!
= (7*6*5! - 2*6*5!)/2
= (42 - 12)*5!/2
= 15*5!
IMO Option C
Calculate the number of ways that 2 shows in city F are done together
= take FF as a single bock
= [FF], A, B, C, D, E
= 6!*2!/2!
So, required number of ways = 7!/2! - 6!*2!/2!
= (7*6*5! - 2*6*5!)/2
= (42 - 12)*5!/2
= 15*5!
IMO Option C
gmatclubot
Re: A folk group wants to have one concert on each of the seven consecutiv [#permalink]
28 Nov 2021, 09:55
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