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A pianist is planning the order in which they will play their recital

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shridhar786
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A pianist is planning the order in which they will play their recital [#permalink] New post  25 May 2019, 23:00
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A pianist is planning the order in which they will play their recital. They will play 6 pieces by 6 different composers: Brahms, Chopin, Haydn, Liszt, Mozart, and Schubert. The recital will be in two halves with 3 pieces before a short interval and 3 pieces straight after. The pianist decides that the final piece in each half will be by one of Liszt, Brahms, or Mozart. How many different possible orders are there for the pianist’s recital?



a) 48
b) 72
c) 120
d)144
e) 720
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LeoN88
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Re: A pianist is planning the order in which they will play their recital [#permalink] New post  25 May 2019, 23:29
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shridhar786 wrote:
A pianist is planning the order in which they will play their recital. They will play 6 pieces by 6 different composers: Brahms, Chopin, Haydn, Liszt, Mozart, and Schubert. The recital will be in two halves with 3 pieces before a short interval and 3 pieces straight after. The pianist decides that the final piece in each half will be by one of Liszt, Brahms, or Mozart. How many different possible orders are there for the pianist’s recital?



a) 48
b) 72
c) 120
d)144
e) 720

Pieces- B C H L M S
Arrangement _ _ _ Interval _ _ _

The two colored spaces can be filled by following ways
LB
BL
BM
MB
LM
ML, rest pieces will be arranged in 4! ways.

So answer: 6*4!= 144 D
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Ishat16189
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Re: A pianist is planning the order in which they will play their recital [#permalink] New post  26 May 2019, 11:56
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B,C,H,L,M,S

P1,P2,P3 interval P4,P5,P6

P3 and P6 can be filled by L,B or M

P3-can be chosen from any one of 3
P6-can be chosen from remaining 2

similarly for remaining 4 places
P1-4
P2-3
P4-2
P5-1

so, 4*3*3*2*1*2 =144
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ScottTargetTestPrep
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A pianist is planning the order in which they will play their recital [#permalink] New post  29 Mar 2021, 10:56
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shridhar786 wrote:
A pianist is planning the order in which they will play their recital. They will play 6 pieces by 6 different composers: Brahms, Chopin, Haydn, Liszt, Mozart, and Schubert. The recital will be in two halves with 3 pieces before a short interval and 3 pieces straight after. The pianist decides that the final piece in each half will be by one of Liszt, Brahms, or Mozart. How many different possible orders are there for the pianist’s recital?



a) 48
b) 72
c) 120
d)144
e) 720

Solution:



The ordering of the musical recital is ___, ___, ___, interval, ___, ___, ___

We see that positions 3 and 6 can be filled by any of 3 composers, so for just those two positions, we have 3P2 = 6 ways to fill them. For the remaining positions (1, 2, 4, and 5), we have 4! = 24 ways to arrange them. Thus, the total number of arrangements of the selections for the recital is 3P2 x 4! = 6 x 24 = 144.

Answer: D
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Re: A pianist is planning the order in which they will play their recital [#permalink] New post  17 Jun 2023, 04:19
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Re: A pianist is planning the order in which they will play their recital [#permalink]
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