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Departments A, B, and C have 10 employees each, and department D has

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Departments A, B, and C have 10 employees each, and department D has  [#permalink]

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New post 16 Jul 2016, 15:01
3
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E

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Departments A, B, and C have 10 employees each, and department D has 20 employees. Departments A, B, C, and D have no employees in common. A task force is to be formed by selecting 1 employee from each of departments A, B, and C and 2 employees from department D. How many different task forces are possible?

A. 19,000
B. 40,000
C. 100,000
D. 190,000
E. 400,000

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Re: Departments A, B, and C have 10 employees each, and department D has  [#permalink]

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New post 16 Jul 2016, 15:49
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Bunuel wrote:
Departments A, B, and C have 10 employees each, and department D has 20 employees. Departments A, B, C, and D have no employees in common. A task force is to be formed by selecting 1 employee from each of departments A, B, and C and 2 employees from department D. How many different task forces are possible?

A. 19,000
B. 40,000
C. 100,000
D. 190,000
E. 400,000


Take the task of creating the task force and break it into stages.

Stage 1: Select one person from department A
There are 10 people to choose from, so we can complete stage 1 in 10 ways

Stage 2: Select one person from department B
There are 10 people to choose from, so we can complete stage 2 in 10 ways

Stage 3: Select one person from department C
There are 10 people to choose from, so we can complete stage 3 in 10 ways

Stage 4: Select 2 people from department D
Since the order in which we select the 2 people does not matter, we can use combinations.
We can select 2 people from 20 people in 20C2 ways (190 ways)
So, we can complete stage 4 in 190 ways

By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus create a task force) in (10)(10)(10)(190) ways (= 190,000 ways)

Answer:

If anyone is interested, here's a video on calculating combinations (like 20C2) in your head

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Re: Departments A, B, and C have 10 employees each, and department D has  [#permalink]

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New post 16 Jul 2016, 15:41
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\(\begin{align}&\text{Department A, B, C}&&10\text{ Employees}&&\text{select }1\\
&\text{Department D}&&20\text{ Employees}&&\text{select }2
\end{align}\)

\(\text{Total }= {10 \choose 1}^3 \times {20 \choose 2} =\\
10^3 \times \frac{20!}{18!\times 2!} =\\
1,000 \times \frac{20 \times 19 \times 18!}{18! \times 2 \times 1} =\\ 1,000 \times \frac{20 \times 19}{2} =\\ 1,000 \times 190 = 190,000\\
\text{Answer: (D) 190,000}\)
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Re: Departments A, B, and C have 10 employees each, and department D has  [#permalink]

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New post 17 Jul 2016, 02:24
10c1 * 10c1* 10c1*20c2 = 10*10*10*190=190,000. Hence D is the correct answer.
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Re: Departments A, B, and C have 10 employees each, and department D has  [#permalink]

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New post 06 Aug 2017, 20:40
Number of ways to choose from Department A,B and C : 10c1 = 10 each

Number of ways to choose from Department D(2 of 20) : 20c2 = 20*19/2 = 190

Total number of task forces possible are : 190*10*10*10 = 190000(Option D)
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Re: Departments A, B, and C have 10 employees each, and department D has  [#permalink]

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New post 09 Aug 2018, 06:45
Doesn't this question require long calculation.
Can GMAT test on this type of question?

Thought the Concept is easy.
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Departments A, B, and C have 10 employees each, and department D has  [#permalink]

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New post 24 Aug 2018, 12:06
Ratnaa19 the calculation is not too long. As long as you realize that you need to multiply 10*10*10*19*10 = 19*10^4 = 190,000 :) Moreover, this question is from one of the exam packs.


quick question: I agree with the possibilities for A, B, C (10*10*10). However, I would like to understand why we need to do D with Combinations and we cannot simply say: XY are two employees from department D (20 employees) so we have 20*19= 380 possibilities

update: I can answer myself: actually if you do 20*19, you would count employee XY and YX twice, but it's the same "pair" so that's why we use combinations :)
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Re: Departments A, B, and C have 10 employees each, and department D has  [#permalink]

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New post 03 Oct 2019, 12:15
Bunuel wrote:
Departments A, B, and C have 10 employees each, and department D has 20 employees. Departments A, B, C, and D have no employees in common. A task force is to be formed by selecting 1 employee from each of departments A, B, and C and 2 employees from department D. How many different task forces are possible?

A. 19,000
B. 40,000
C. 100,000
D. 190,000
E. 400,000


The number of ways to select 1 employee from each of departments A, B, and C and 2 employees from department D is

10C1 x 10C1 x 10C1 x 20C2 = 10 x 10 x 10 x (20 x 19)/2 = 10 x 10 x 10 x 10 x 19 = 190,000

Answer: D
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Re: Departments A, B, and C have 10 employees each, and department D has   [#permalink] 03 Oct 2019, 12:15
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