Permutations and Combination

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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pm; Followed by:6 members

Permutations and Combination

by BTGmoderatorRO » Sun Jan 07, 2018 2:04 am

How many different groups of 3 people can be formed from a group of 5 people?

A. 5
B. 6
C. 8
D. 9
E. 10

OA is E
Are there different methods to solve this? An Expert pls.

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Source: Beat The GMAT — Problem Solving | Sun Jan 07, 2018 2:04 am

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

by Brent@GMATPrepNow » Sun Jan 07, 2018 7:34 am

Roland2rule wrote:How many different groups of 3 people can be formed from a group of 5 people?

A. 5
B. 6
C. 8
D. 9
E. 10

Since the order in which we select the 3 people does not matter, we can use COMBINATIONS

We can select 3 people from 5 people in 5C3 ways

5C3 = (5)(4)(3)/(3)(2)(1) = 10

Answer: E

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 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Sun Jan 07, 2018 4:48 pm

Hi Roland2rule,

We're asked for the number of different groups of 3 people that can be formed from a group of 5 people. Using the Combination Formula is arguably the fastest way to answer this question (as Brent has shown). You'll notice that the answer choices are relatively small though, so you could just 'map out' all of the possibilities.

If we name the 5 people: A, B, C, D and E, then the groups would be...
ABC
ABD
ABE
ACD
ACE
ADE
BCD
BCE
BCE
CDE

Total Groups = 10

Final Answer: E

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

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Aug 04, 2019 10:31 am

BTGmoderatorRO wrote:How many different groups of 3 people can be formed from a group of 5 people?

A. 5
B. 6
C. 8
D. 9
E. 10

OA is E
Are there different methods to solve this? An Expert pls.

The number of groups of 3 that can be formed from 5 people is 5C3 = (5 x 4 x 3)/3! = 10.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]