Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Christina scored 760 by having clear (ability) milestones and a trackable plan to achieve the same. Attend this webinar to learn how to build trackable milestones that leverage your strengths to help you get to your target GMAT score.
The Easter Bunny brings … the first day of school?? Yes! Now is the time to start studying for the GMAT if you’re planning to apply to Round 1 of fall MBA programs. Get a special discount with the Easter sale!
$84 + an extra $10 off for the first month of EMPOWERgmat access. Train to be ready for Round 3 Deadlines with EMPOWERgmat's Score Booster. Ends April 21st Code: GCENHANCED
What people who reach the high 700's do differently? We're going to share insights, tips, and strategies from data we collected on over 50,000 students who used examPAL. Save your spot today!
An office comprised of eight employees is planning to have a foosball
[#permalink]
Show Tags
31 Jul 2017, 23:57
1
6
00:00
A
B
C
D
E
Difficulty:
95% (hard)
Question Stats:
20% (01:43) correct 80% (02:15) wrong based on 100 sessions
HideShow timer Statistics
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?
Re: An office comprised of eight employees is planning to have a foosball
[#permalink]
Show Tags
13 Aug 2017, 08:21
2
Top Contributor
3
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
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)
Re: An office comprised of eight employees is planning to have a foosball
[#permalink]
Show Tags
01 Aug 2017, 00:00
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?
Re: An office comprised of eight employees is planning to have a foosball
[#permalink]
Show Tags
12 Aug 2017, 23:52
Don't know if my reasoning is right, but here's my take: Every match is done with 4 people, so we have to find out in how many ways we can split up those 8 in groups of 4: 8C4. Now that we have 2 groups of 4, separate them in pairs: 4C2. Thing is, do we have pair A, B, etc? I may be wrong, but I don't we do, so:
Re: An office comprised of eight employees is planning to have a foosball
[#permalink]
Show Tags
26 Aug 2017, 15:12
First, recognize that picking 4 people from a group of 8 (to create a single match up) is simply: 8*7*6*5, aka 8!/(8-4)!
Then, realize the number of redundant groupings: 1. Team A can be (1,2) or (2,1) 2. Team B can be (3,4) or (4,3) 3. Team A vs Team B is another redundancy (A,B) or (B,A)
So, you end up with (8*7*6*5)/(2!*2!*2!)
At this point, I like to break down 8*7*6*5 to primes: (2^4*7*3*5)
This, divided by 2^3 leads to: 7*3*2*5 = 21*10 = 210
Re: An office comprised of eight employees is planning to have a foosball
[#permalink]
Show Tags
26 Aug 2017, 19:58
GMATPrepNow wrote:
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
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)
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.
RELATED VIDEOS
Thanks for the great explanation. But I have a doubt. For stage two you have considered only the first 4 employees a,b,c,d and not the rest e,f,g,h. Does it mean, if we get the no. of ways for just 4 employees and multiply it by the stage 1's 70, then we automatically consider the rest four(e,f,g,h)?
An office comprised of eight employees is planning to have a foosball
[#permalink]
Show Tags
26 Aug 2017, 20:35
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
Hi..
the Q would be a simple combinations BUT for pairs..
If you understand that when you take out TWO out of FOUR, the OTHER 2 automatically make a PAIR, you have your answer.
Choose 4 out of 8 in 8C4. Now choose two out of these 4 in 4C2 ways, but divide by 2! because of the reason mentioned above.. EXAMPLE 4 person ABCD.. way to choose two is 4C2 but this includes AB and CD as 2 different cases.. However when you choose AB, you are automically making other two CD as a pair.
ans = \(8C4*4C2*\frac{1}{2!}=\frac{8!}{4!*4!}*\frac{4!}{2!2!}*\frac{1}{2}=\frac{8*7*6*5}{8}=210\) B
_________________
Re: An office comprised of eight employees is planning to have a foosball
[#permalink]
Show Tags
17 Mar 2019, 04:39
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
close
20% (01:43) correct 
