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16 Jul 2016, 15:01
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
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Question Stats:
84% (01:24) correct
16%
(01:55)
wrong
based on 759
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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
A. 19,000
B. 40,000
C. 100,000
D. 190,000
E. 400,000
16 Jul 2016, 15:49
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Bunuel
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
16 Jul 2016, 15:41
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\(\begin{align}&\text{Department A, B, C}&&10\text{ Employees}&&\text{select }1\\\\
&\text{Department D}&&20\text{ Employees}&&\text{select }2\\
\end{align}\)
\(\text{Total }= {10 \choose 1}^3 \times {20 \choose 2} =\\\\
10^3 \times \frac{20!}{18!\times 2!} =\\\\
1,000 \times \frac{20 \times 19 \times 18!}{18! \times 2 \times 1} =\\ 1,000 \times \frac{20 \times 19}{2} =\\ 1,000 \times 190 = 190,000\\\\
\text{Answer: (D) 190,000}\)
&\text{Department D}&&20\text{ Employees}&&\text{select }2\\
\end{align}\)
\(\text{Total }= {10 \choose 1}^3 \times {20 \choose 2} =\\\\
10^3 \times \frac{20!}{18!\times 2!} =\\\\
1,000 \times \frac{20 \times 19 \times 18!}{18! \times 2 \times 1} =\\ 1,000 \times \frac{20 \times 19}{2} =\\ 1,000 \times 190 = 190,000\\\\
\text{Answer: (D) 190,000}\)
Moreover, this question is from one of the exam packs.
