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Probability question from Kaplan Cat test

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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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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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