How many ways are possible to arrange A, B, C, C, and D with

Question

How many ways are possible to arrange A, B, C, C, and D with two "C" being separated by at least one letter?

NightAlum · Answer

I get 36

Perms:
CACBD - 6 possibilities
CABCD - 6
CABDC-6
ACBCD-6
ACBDC-6
ABCDC-6

6*6 = 36

However if Cs are distinct (which is probably  not  what the question implies), the answer would be 72.

iruns0metimes · Answer

C _ C _ _
C _ _ C _
C _ _ _ C
_ C _ C _
_ C _ _ C
_ _ C _ C

In each of these, we have 3 blanks, the contents of which are completely up for variation (thus it is a factorial).

3! = 3*2*1 = 6 possibilities for each of the patterns above

6*6 =  36

Another note:
--Since the C's are the same, we don't need to account for switching the two C's in each case above.

rpmodi · Answer

I get 96 (5!-4!) , is that correct?

5! = number of ways to arrange A,B,C,C,D 
4! = assuming CC are consecutive

so Number of ways such that C,C are atlease one space apart is 5!-4!=96

walker · Answer

5! corresponds to 5 different things but here we have the same two things and 3 different. So, the correct total number of ways to arrange A,B,C,C,D will be 5!/2. ( A,B,C_1,C_2,D  and  A,B,C_2,C_1,D  is the same combination)

5!/2-4!=60-24=36

rpmodi · Answer

sorry , my answer is 36 as well

it should be 5!/2 - 4! ( 5!/2 since we have a repetition of C )

How many ways are possible to arrange A, B, C, C, and D with

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