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

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

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New post 01 Jul 2018, 02:14
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A
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E

Difficulty:

  55% (hard)

Question Stats:

60% (01:46) correct 40% (01:26) wrong based on 52 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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Re: Jean is arranging paint brushes used by artists for an impressionist's  [#permalink]

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New post 01 Jul 2018, 08:09
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

Answer is 15!/(5!3!4!2!)
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Re: Jean is arranging paint brushes used by artists for an impressionist's  [#permalink]

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New post 01 Jul 2018, 12:22
E is the answer.

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!)
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Re: Jean is arranging paint brushes used by artists for an impressionist's  [#permalink]

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New post 01 Jul 2018, 12:52
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!)

Answer E.


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Re: Jean is arranging paint brushes used by artists for an impressionist's  [#permalink]

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New post 01 Jul 2018, 16:31
4 van Gogh is "1"
VmmmmmMMMddddtt
Formula:
(1+5+3+4+2)! / (1!5!3!4!2!)
Answer E
Re: Jean is arranging paint brushes used by artists for an impressionist's &nbs [#permalink] 01 Jul 2018, 16:31
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