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An office comprised of eight employees is planning to have a
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08 Oct 2017, 22:44
08 Oct 2017, 22:44
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Question Stats:
28% (02:32) correct
71% (02:12) wrong based on 7 sessions
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An office comprised of eight employees is planning to have a foosball game. A matchup consists of four players, split into pairs. If any employee can be paired up with any other employee, then how many unique matchups result?
(A) 70
(B) 210
(C) 280
(D) 336
(E) 420
Kudos for correct solution.
(A) 70
(B) 210
(C) 280
(D) 336
(E) 420
Kudos for correct solution.
Re: An office comprised of eight employees is planning to have a
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09 Oct 2017, 00:09
09 Oct 2017, 00:09
1
Bunuel wrote:
An office comprised of eight employees is planning to have a foosball game. A matchup consists of four players, split into pairs. If any employee can be paired up with any other employee, then how many unique matchups result?
Here, first we need to choose 4 employess from 8
i.e 8C4
Now these 4 employess split into 2 and can be paired with any one -
Let us have Ann, Bob, Dan and Jack as four employees
Now to pair up Ann we have three option left i.e Bob, Dan and Jack
So we have three possible ways.
There fore total ways = 8C4 * 3 = 70 * 3 = 210 ways.
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Re: An office comprised of eight employees is planning to have a
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21 Sep 2021, 09:18
21 Sep 2021, 09:18
1
Bunuel wrote:
An office comprised of eight employees is planning to have a foosball game. A matchup consists of four players, split into pairs. If any employee can be paired up with any other employee, then how many unique matchups result?
(A) 70
(B) 210
(C) 280
(D) 336
(E) 420
Kudos for correct solution.
(A) 70
(B) 210
(C) 280
(D) 336
(E) 420
Kudos for correct solution.
Take the task of creating a matchup and break it into stages.
Stage 1: Select 4 employees
Since the order in which we select the employees does not matter, we can use combinations.
We can select 4 employees from 8 employees in 8C5 ways (70 ways)
So, we can complete stage 1 in 70 ways
Stage 2: Divide the 4 selected employees into 2 teams
Let's say the 4 selected employees are A, B, C, D
A nice way to determine the number of ways to divide the 4 employees into 2 teams is to find a partner for one person.
For example, let's find a partner for employee A.
NOTE: once we choose a partner for employee A then, by default, the remaining two two employees will be paired together.
In how many ways can we select a partner for employee A? Well, A can be paired with B, C or D
So, we can complete stage 2 in 3 ways
ASIDE: The 3 pairings are:
AB vs CD
AC vs BD
AD vs BC
By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create a matchup) in (70)(3) ways (= 210 ways)
Answer: B
