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# Jean is arranging paint brushes used by artists for an impressionist's

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Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 984
Location: India
GPA: 3.64
Jean is arranging paint brushes used by artists for an impressionist's  [#permalink]

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01 Jul 2018, 01:14
1
2
00:00

Difficulty:

45% (medium)

Question Stats:

66% (02:07) correct 34% (01:57) wrong based on 58 sessions

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Jean is arranging paint brushes used by artists for an impressionist's exhibit. He has 4 from Van Gogh, 5 from Monet, 3 from Manet, 4 from Degas, and 2 from Toulouse-Lautrec to choose from. All brushes from the same artist are considered identical for ordering. Jean wants to group all the brushes from Van Gogh together. How many ways can he arrange the paint brushes by the artist that used them?
A) 5!
B) 15!
C) $$\frac{15!}{4!}$$
D) $$\frac{11!}{5!3!4!2!}$$
E) $$\frac{15!}{5!3!4!2!}$$

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Joined: 28 Jul 2016
Posts: 134
Re: Jean is arranging paint brushes used by artists for an impressionist's  [#permalink]

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01 Jul 2018, 07:09
If we don't care of order, that group of Van Gogh brushes can be counted as 1 item
So, in this case we have:
Van Gogh = 1
Monet = 5
Manet = 3
Degas = 4
Toulouse-Lautrec = 2

Total ways to arrange 15 items = (1 + 5 + 3 + 4 + 2)! = 15!
As order doesn't matter we should multiply by factorial of number of each repeating group

Intern
Joined: 19 Nov 2017
Posts: 16
Re: Jean is arranging paint brushes used by artists for an impressionist's  [#permalink]

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01 Jul 2018, 11:22

This is a permutation question and the order is important.
Van Gogh brushes is considered as 1 entity.
So we have Van Gogh = 1,Monet = 5,Manet = 3,Degas = 4 and Toulouse-Lautrec = 2
So N = (1 + 5 + 3 + 4 + 2) = 15

Total arrangements = n!/(p!+q!+...) so soln is : 15!/(5!*3!*4!*2!)
Director
Joined: 14 Dec 2017
Posts: 518
Location: India
Re: Jean is arranging paint brushes used by artists for an impressionist's  [#permalink]

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01 Jul 2018, 11:52
souvonik2k wrote:
Jean is arranging paint brushes used by artists for an impressionist's exhibit. He has 4 from Van Gogh, 5 from Monet, 3 from Manet, 4 from Degas, and 2 from Toulouse-Lautrec to choose from. All brushes from the same artist are considered identical for ordering. Jean wants to group all the brushes from Van Gogh together. How many ways can he arrange the paint brushes by the artist that used them?
A) 5!
B) 15!
C) $$\frac{15!}{4!}$$
D) $$\frac{11!}{5!3!4!2!}$$
E) $$\frac{15!}{5!3!4!2!}$$

Consider the 4 Van Gogh brushes as 1 unit, since they need to be grouped together.

Hence we have Total # of brushes = 1 + 5 + 3 + 4 + 2 = 15

So we have total # of ways to arrange the brushes = 15!/(5!3!4!2!)

Thanks,
GyM
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Posts: 188
Re: Jean is arranging paint brushes used by artists for an impressionist's  [#permalink]

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01 Jul 2018, 15:31
4 van Gogh is "1"
VmmmmmMMMddddtt
Formula:
(1+5+3+4+2)! / (1!5!3!4!2!)
Re: Jean is arranging paint brushes used by artists for an impressionist's &nbs [#permalink] 01 Jul 2018, 15:31
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