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# John must arrange 3 different physics books and 3 different mathematic

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Math Expert
Joined: 02 Sep 2009
Posts: 54496
John must arrange 3 different physics books and 3 different mathematic  [#permalink]

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14 Jun 2016, 02:37
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Difficulty:

15% (low)

Question Stats:

81% (01:34) correct 19% (02:01) wrong based on 150 sessions

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John must arrange 3 different physics books and 3 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist?

A. 6
B. 9
C. 36
D. 120
E. 720

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Math Expert
Joined: 02 Aug 2009
Posts: 7588
Re: John must arrange 3 different physics books and 3 different mathematic  [#permalink]

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14 Jun 2016, 03:12
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1
Bunuel wrote:
John must arrange 3 different physics books and 3 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist?

A. 6
B. 9
C. 36
D. 120
E. 720

First place the maths book -
since all are different books, they can be arranged in 3! ways - 6 ways...

next we have 4 places for physics book, but leftmost is not a valid place as left is always maths..
_M_M_M_, but valid ways are M_M_M_
so 3 places for 3 books - again 3! ways...

Total = $$3!*3! = 36$$

C
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Joined: 05 Sep 2015
Posts: 43
Re: John must arrange 3 different physics books and 3 different mathematic  [#permalink]

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14 Jun 2016, 03:24
3! *3 ! = 36
three maths can me arranged 3!ways, 3 physics books in 3! ways
Manager
Joined: 12 Oct 2012
Posts: 112
WE: General Management (Other)
Re: John must arrange 3 different physics books and 3 different mathematic  [#permalink]

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14 Jun 2016, 04:42
1
First Place, is reserved for Math book. There are 3 Math books which can be arranged in 3 ways

Restriction comes into play hysics book cannot be together. Hence, the math & the physics books take alternate places

Second Place, Physics Book - in 3 ways
Third Place, Math Book - in 2 ways (only 2 books left)
Fourth Place, Physics - in 2 ways (only 2 Physics book left)
Rest two places can be arranged in one way only.

Total no of ways = 3*3*2*2*1*1 = 36 ways
Director
Joined: 21 Mar 2016
Posts: 519
Re: John must arrange 3 different physics books and 3 different mathematic  [#permalink]

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14 Jun 2016, 07:25
leftmost is reserved for math book so the pattern is M _M_M_
consider maths book first,,they can be placed in 3*2*1 =3! ways
then, physics book can be placed in 3! ways
total ways = 3! *3! = 36
option c
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Joined: 09 Sep 2013
Posts: 10625
Re: John must arrange 3 different physics books and 3 different mathematic  [#permalink]

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23 Mar 2019, 05:54
Hello from the GMAT Club BumpBot!

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Re: John must arrange 3 different physics books and 3 different mathematic   [#permalink] 23 Mar 2019, 05:54
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