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# A team of construction workers must include two masons, three carpente

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Math Expert
Joined: 02 Sep 2009
Posts: 52296
A team of construction workers must include two masons, three carpente  [#permalink]

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27 Apr 2017, 01:19
00:00

Difficulty:

25% (medium)

Question Stats:

81% (02:04) correct 19% (02:34) wrong based on 53 sessions

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A team of construction workers must include two masons, three carpenters, four electricians, and two plumbers. If the job foreman has six possible choices from each profession to choose from, how many different teams could the foreman create?

A. 2,496,144
B. 135,000
C. 629,856
D. 67,500
E. 6,750

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Re: A team of construction workers must include two masons, three carpente  [#permalink]

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27 Apr 2017, 03:07
The way to choose 2 masons from 6 is 6c2
The way to choose 3 masons from 6 is 6c3
The way to choose 4 electricians from 6 is 6c4
The way to choose 2 plumbers from 6 is 6c2
Total possibilities are 6c2 * 6c3 * 6c4 * 6c2 = 67500(Option D)
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Re: A team of construction workers must include two masons, three carpente  [#permalink]

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02 May 2017, 15:45
Bunuel wrote:
A team of construction workers must include two masons, three carpenters, four electricians, and two plumbers. If the job foreman has six possible choices from each profession to choose from, how many different teams could the foreman create?

A. 2,496,144
B. 135,000
C. 629,856
D. 67,500
E. 6,750

We are given that a team of construction workers must include two masons, three carpenters, four electricians, and two plumbers. If the job foreman has six possible choices, then:

The number of ways to choose 2 masons = 6C2 = (6 x 5)/2! = 15

The number of ways to choose 3 carpenters = 6C3 = (6 x 5 x 4)/3! = (6 x 5 x 4)(3 x 2) = 20

The number of ways to choose 4 electricians = 6C4 = (6 x 5 x 4 x 3)/4! = (6 x 5 x 4 x 3)(4 x 3 x 2) = 15

The number of ways to choose 2 plumbers = 6C2 = (6 x 5)/2! = 15

Thus, the total number of teams that can be formed is 15 x 20 x 15 x 15 = 67,500.

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Re: A team of construction workers must include two masons, three carpente &nbs [#permalink] 02 May 2017, 15:45
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