Some fourth graders are choosing foursquare teams at

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Thu May 03, 2018 10:32 am

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Some fourth graders are choosing foursquare teams at recess. What is the total possible number of combinations of four-person teams that could be chosen from a group of six kids?

(A) 6
(B) 15
(C) 120
(D) 360
(E) 98,280

The OA is the option B.

What is the formula that I should use here? May someone helps me? Please.

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Source: Beat The GMAT — Problem Solving | Thu May 03, 2018 10:32 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu May 03, 2018 2:39 pm

VJesus12 wrote:Some fourth graders are choosing foursquare teams at recess. What is the total possible number of combinations of four-person teams that could be chosen from a group of six kids?

(A) 6
(B) 15
(C) 120
(D) 360
(E) 98,280

This is a somewhat ambiguous question since it's hard to tell whether each team member's position matters.
For example, if the question were rephrased to ask how many 9-person baseball teams can be created from 9 people, we might say the correct answer is 1.
However, if we consider the different positions that each player can have, we could also say the correct answer is 9!

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Thu May 03, 2018 4:32 pm

Hi VJesus12,

We're asked for the total possible number of combinations of four-person foursquare teams that could be chosen from a group of six kids. I agree with Brent's assessment (it's not perfectly clear whether we're supposed to be treating this question as a Permutation or a Combination). That having been said, the 'intent' of this question is that it's meant to be a Combination Formula question:

N!/(K!)(N-K)! where N is the total number of people and K is the size of the 'subgroup'

With 6 children and a group of 4, we have.... 6!/(4!)(2!) = (6)(5)/(2)(1) = 15 possible groups of 4.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon May 07, 2018 10:15 am

VJesus12 wrote:Some fourth graders are choosing foursquare teams at recess. What is the total possible number of combinations of four-person teams that could be chosen from a group of six kids?

(A) 6
(B) 15
(C) 120
(D) 360
(E) 98,280

The number of ways 4 people can be chosen from 6 people is 6C4 = 6!/(4! x 2!) = (6 x 5)/( 2) = 30/2 = 15.

Answer: B

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