Probability question from Kaplan Cat test

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hwiya320: Senior | Next Rank: 100 Posts; Posts: 93; Joined: Tue Sep 02, 2008 5:34 pm; Thanked: 7 times

by hwiya320 » Tue Nov 25, 2008 8:38 pm

In how many different ways can the letters A, A, B, B. B, C, D, E be arranged if the letter C must be to the right of the letter D?

1,680
2,160
2,520
3,240
3,360

Answer A

Im hoping to get a clear understanding of this question..

Thanks!

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Source: Beat The GMAT — Problem Solving | Tue Nov 25, 2008 8:38 pm

agoyal2: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Fri Feb 29, 2008 9:00 am; Thanked: 4 times

by agoyal2 » Sun Nov 30, 2008 1:28 am

Total number of ways of arranging 8 letters = 8!

Since A is repeated twice and B is repeated thrice, their order does not matter, hence divide 8! by 2! (ways of arranging two A's) and 3! (Ways of arranging B's).

Now, D must be right of C. Out of all the combinations, half of them will have D in the right of C and half in the left.

So, final answer = (8!)/(2!*3!*2)

Hope this helps

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