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# A company wants to have each of 9 of its employees work on painting ex

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Math Expert
Joined: 02 Sep 2009
Posts: 51122
A company wants to have each of 9 of its employees work on painting ex  [#permalink]

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08 Jul 2018, 20:32
00:00

Difficulty:

45% (medium)

Question Stats:

63% (02:06) correct 37% (03:06) wrong based on 41 sessions

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A company wants to have each of 9 of its employees work on painting exactly one of the three rooms P, Q, and R. If 2 of these employees are to work on painting room P, 3 of these employees are to work on painting room Q , and 4 of these employees are to work on painting room R, then in how many different ways can these 9 employees be given rooms to paint?

A. 1,008

B. 1,260

C. 1,680

D. 1,890

E. 5,184

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Director
Joined: 14 Dec 2017
Posts: 519
Location: India
A company wants to have each of 9 of its employees work on painting ex  [#permalink]

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08 Jul 2018, 21:31
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Bunuel wrote:
A company wants to have each of 9 of its employees work on painting exactly one of the three rooms P, Q, and R. If 2 of these employees are to work on painting room P, 3 of these employees are to work on painting room Q , and 4 of these employees are to work on painting room R, then in how many different ways can these 9 employees be given rooms to paint?

A. 1,008

B. 1,260

C. 1,680

D. 1,890

E. 5,184

Given 9 employees, to be divided into three groups of 2 employees, 3 employees & 4 employees, each to paint rooms P, Q & R respectively.

# of ways of dividing them = $$\frac{9!}{(2!*3!*4!)}$$ = $$1260$$

Using the formula, if we have (m+n+p) objects & we have to divide them into 3 groups of m, n & p objects. then

# of ways of dividing them = $$\frac{(m + n + p)!}{(m!*n!*p!)}$$

Alternate approach:

Select first 2 employees out of 9 = 9C2

next Select 3 employees out of 7 remaining = 7C3

finally the remaining 4 will be part of last group of 4, hence 4C4

# of ways of dividing them into the groups = 9C2 * 7C3 * 4C4 = 1260

Thanks,
GyM
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Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Re: A company wants to have each of 9 of its employees work on painting ex  [#permalink]

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09 Jul 2018, 04:19
Bunuel wrote:
A company wants to have each of 9 of its employees work on painting exactly one of the three rooms P, Q, and R. If 2 of these employees are to work on painting room P, 3 of these employees are to work on painting room Q , and 4 of these employees are to work on painting room R, then in how many different ways can these 9 employees be given rooms to paint?

A. 1,008

B. 1,260

C. 1,680

D. 1,890

E. 5,184

P------------Q------------R
2------------3------------4
No of ways 9 employees can be given rooms P,Q & R=No of ways 2 employees can be given room P* No of ways 3 employees can be given room Q out of remaining 7 employees*No of ways 4 employees can be given room R out of remaining 4 employees
=9C2*7C3*4C4=1260

Ans.(B)
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Regards,

PKN

Rise above the storm, you will find the sunshine

Re: A company wants to have each of 9 of its employees work on painting ex &nbs [#permalink] 09 Jul 2018, 04:19
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