Count number of ways to arrange 4 people A, B, C, D in a row so that C

Question

Count number of ways to arrange 4 people A, B, C, D in a row so that C, D not sit next to each other

A, 6
B. 12
C. 18
D. 24
E. 30

nick1816 · Answer

number of ways to arrange 4 people A, B, C, D in a row=4!=24
number of ways to arrange 4 people A, B, C, D in a row, when C and D sit next to each other= 2*3!=12
number of ways to arrange 4 people A, B, C, D in a row, when C and D are not sitting next to each other= 24-12=12

LevanKhukhunashvili · Answer

First count without restriction:
4 people in a row, 4!=24 ways

now count the ways that are restricted:
CD as one person as they must seat to next each other and other two persons A and B, 3!=6
Note that CD order is different from DC, so multiply 6 by 2 and get 12

So total arrangements with restriction will be 24-12=12

IMO
Ans:  B

Archit3110 · Answer

ABCD
CD=X; 2! WAYS
XAB ; 3! WAYS
3!*2! ; 12
IMO B

CareerGeek · Answer

Number of ways of not sitting together = Total ways - When both sit together

Total ways = 4! = 24 ways

When C&D are together—> CD, A, B (consider C&D as one unit)
Number of ways = 3!*2! = 6*2 = 12 ways

Not together = 24 - 12 = 12 ways

Option B.

Pls Hit kudos if you like the solution

Posted from my mobile device

akankshaboparai · Answer

No of ways to arrange people = 4! = 24 ways.

Bunuel .. Can we consider the case that half of the time CD will sit together and the other half they won't? So then the answer will be 12?

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Count number of ways to arrange 4 people A, B, C, D in a row so that C

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Count number of ways to arrange 4 people A, B, C, D in a row so that C

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards