GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 24 Jan 2020, 00:31

### GMAT Club Daily Prep

#### 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

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

# At a high school track tryout, there are eight women and five men comp

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 02 Jan 2017
Posts: 290
At a high school track tryout, there are eight women and five men comp  [#permalink]

### Show Tags

24 Feb 2017, 09:41
2
00:00

Difficulty:

5% (low)

Question Stats:

86% (01:25) correct 14% (01:34) wrong based on 96 sessions

### HideShow timer Statistics

At a high school track tryout, there are eight women and five men competing for the three male and three female spots on the decathlon team. How many different combinations of decathletes are possible on the final team for the six spots?

(A) 112,896
(B) 3,136
(C) 560
(D) 66
(E) 18
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4476
Re: At a high school track tryout, there are eight women and five men comp  [#permalink]

### Show Tags

24 Feb 2017, 16:58
1
vikasp99 wrote:
At a high school track tryout, there are eight women and five men competing for the three male and three female spots on the decathlon team. How many different combinations of decathletes are possible on the final team for the six spots?

(A) 112,896
(B) 3,136
(C) 560
(D) 66
(E) 18

Dear vikasp99,

I'm happy to respond. Like most Veritas questions, this is a great question. For computing combinations, see these two posts:
GMAT Permutations and Combinations
GMAT Math: Calculating Combinations

For the females, we have 8 women competing for three spots.
$$8C3 = \frac{8!}{(5!)(3!)} = \frac{8*7*6}{3*2*1} = 8*7 = 56$$

For the males, we have 5 men competing for three spots.
$$5C3 = \frac{5!}{(2!)(3!)} = \frac{5*4}{2} = 10$$

Any male set of three can be paired with any female set of three, so we multiply, because of the Fundamental Counting Principle.
total number = 56*10 = 560

OA = (C)

Does all this make sense?
Mike
_________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Intern
Joined: 31 Aug 2017
Posts: 3
Re: At a high school track tryout, there are eight women and five men comp  [#permalink]

### Show Tags

02 Sep 2017, 14:15
I dont get the last step 56*10. What in the question suggests they are paired?

Sent from my SM-G360H using GMAT Club Forum mobile app
Math Expert
Joined: 02 Sep 2009
Posts: 60630
Re: At a high school track tryout, there are eight women and five men comp  [#permalink]

### Show Tags

03 Sep 2017, 04:31
churchntj wrote:
I dont get the last step 56*10. What in the question suggests they are paired?

Sent from my SM-G360H using GMAT Club Forum mobile app

We multiply because of FUNDAMENTAL PRINCIPLE OF COUNTING (Mike above mentions it and gives a link to the article explaining it), which states if an operation can be performed in ‘m’ ways and when it has been performed in any of these ways, a second operation that can be performed in ‘n’ ways then these two operations can be performed one after the other in ‘m*n’ ways.

We have 6 spots to fill (3 male and 3 female). We can choose 3 females from 8 in 56 ways and we can choose 3 males from 5 in 10 ways, thus according to the FPC the total number of ways to fill 6 spots is 56*10.

Check the links below:

21. Combinatorics/Counting Methods

For more:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 14003
Re: At a high school track tryout, there are eight women and five men comp  [#permalink]

### Show Tags

03 Dec 2019, 11:43
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.
_________________
Re: At a high school track tryout, there are eight women and five men comp   [#permalink] 03 Dec 2019, 11:43
Display posts from previous: Sort by

# At a high school track tryout, there are eight women and five men comp

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne