problem solving: combinations

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fiza gupta: Master | Next Rank: 500 Posts; Posts: 216; Joined: Sun Jul 31, 2016 9:55 pmFollowed by: 7 members; Location: Punjab; Thanked: 31 times

by fiza gupta » Mon Sep 19, 2016 11:54 pm

There are four distinct pairs of brothers and sisters. In how many ways can a committee of 3 be formed and not have siblings in it?

(A) 8
(B) 24
(C) 32
(D 56
(E) 80

Fiza Gupta

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Source: Beat The GMAT — Problem Solving | Mon Sep 19, 2016 11:54 pm

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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 » Tue Sep 20, 2016 4:57 am

fiza gupta wrote:There are four distinct pairs of brothers and sisters. In how many ways can a committee of 3 be formed and not have siblings in it?

(A) 8
(B) 24
(C) 32
(D 56
(E) 80

Take the task of creating a committee and break it into stages.

NOTE: Let's call a brother-sister pair a FAMILY

Stage 1: Select 3 FAMILIES
Since the order in which we select the families does not matter, we can use COMBINATIONS
We can select 3 families from 4 families in 4C3 ways ( = 4 ways)

ASIDE: If anyone is interested, we have a video on calculating combinations (like 4C3) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789

At this point, we have 3 FAMILIES, which we'll call A, B and C. We're now going to select ONE person from each family to be on the committee.

Stage 2: Select 1 person from family A
There are 2 people in this family, so we can complete this stage in 2 ways.

Stage 3: Select 1 person from family B
There are 2 people in this family, so we can complete this stage in 2 ways.

Stage 4: Select 1 person from family C
There are 2 people in this family, so we can complete this stage in 2 ways.

By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus create a 3-person committee) in (4)(2)(2)(2) ways ([spoiler]= 32 ways[/spoiler])

Answer: C
--------------------------

Note: the FCP can be used to solve the majority of counting questions on the GMAT. For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat-counting?id=775

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
- https://www.beatthegmat.com/counting-pro ... 44302.html
- https://www.beatthegmat.com/picking-a-5- ... 73110.html
- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html
- https://www.beatthegmat.com/mouse-pellets-t274303.html

MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
- https://www.beatthegmat.com/arabian-hors ... 50703.html
- https://www.beatthegmat.com/sub-sets-pro ... 73337.html
- https://www.beatthegmat.com/combinatoric ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
- https://www.beatthegmat.com/combinatoric ... 67079.html

DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
- https://www.beatthegmat.com/ps-counting-t273659.html
- https://www.beatthegmat.com/permutation- ... 73915.html
- https://www.beatthegmat.com/please-solve ... 71499.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/laniera-s-co ... 15764.html

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMAT/MBA Expert

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 » Tue Sep 20, 2016 4:59 am

Here's a similar question to practice with: https://www.beatthegmat.com/if-a-committ ... 92338.html

Brent Hanneson - Creator of GMATPrepNow.com

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