In how many different ways can 3 identical green shirts and 3 identical red shirts be distributed among 6 children such that each child receives a shirt?
A. 20
B. 40
C. 216
D. 720
E. 729
OA A
Source: Magoosh
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
In how many different ways can 3 identical green shirts and
This topic has expert replies
-
BTGmoderatorDC
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
GMAT/MBA Expert
-
Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
If there are p numbers of identical items, q numbers of identical items, and r numbers of identical items, the total number of way, (p + q + r) items be distributed is given by (p + q + r)! / (p!*q!*r!).BTGmoderatorDC wrote:In how many different ways can 3 identical green shirts and 3 identical red shirts be distributed among 6 children such that each child receives a shirt?
A. 20
B. 40
C. 216
D. 720
E. 729
OA A
Source: Magoosh
Thus, the number of ways 3 identical green shirts and 3 identical red shirts be distributed among 6 children = 6! / 3!*3! = 20
The correct answer: A
Hope this helps!
-Jay
_________________
Manhattan Review GMAT Prep
Locations: GMAT Manhattan | GRE Prep Courses Austin | ACT Tutoring Tampa | Chicago IELTS Tutoring | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
GMAT/MBA Expert
-
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
We can take this question and ask an easier question: In how many ways can we choose 3 of the 6 children to receive a green shirt?BTGmoderatorDC wrote:In how many different ways can 3 identical green shirts and 3 identical red shirts be distributed among 6 children such that each child receives a shirt?
A. 20
B. 40
C. 216
D. 720
E. 729
Notice that, once we have given a green shirt to each of those 3 chosen children, the remaining children must get red shirts. In other words, once we have given green shirts to 3 children, the children who get red shirts is locked.
So, in how many ways can we select 3 of the 6 children to receive a green shirt?
Since the order of the selected children does not matter, this is a combination question.
We can choose 3 children from 6 children in 6C3 ways (= 20 ways)
Answer: A
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
1st Child: 6 has options
2nd Child: 5 has options...
Therefore, for all kids: \(6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 = 720\) arrangements.
Since the reds are identical, we divide by \(3!\); Since the greens are identical, we divide by another \(3!\)
So: in all, \(\frac{720}{3! \cdot 3!} = 20\) ways.
2nd Child: 5 has options...
Therefore, for all kids: \(6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 = 720\) arrangements.
Since the reds are identical, we divide by \(3!\); Since the greens are identical, we divide by another \(3!\)
So: in all, \(\frac{720}{3! \cdot 3!} = 20\) ways.
