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ajay_gmat
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In how many ways can you arrange the word INDEPENDENCE such 17 Jul 2007, 09:07
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In how many ways can you arrange the word INDEPENDENCE such that the Ds and the Es are always together.. ??

Please solve :-D



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In how many ways can you arrange the word INDEPENDENCE such Updated on: 18 Jul 2007, 09:07
Originally posted by wudy on 17 Jul 2007, 20:17.
Last edited by wudy on 18 Jul 2007, 09:07, edited 2 times in total.
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ajay_gmat
In how many ways can you arrange the word INDEPENDENCE such that the Ds and the Es are always together.. ??

Please solve :-D
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There are two 'D' and four 'E', so the arrangement must be that 'D' is always in the middle of 'E'--'EDE'-- and hence that there are two 'EDE', three 'N', and one 'I', 'P', and 'C'.

Therefore, 8!/(3!*2!).

Find I am wrong. Revise... :oops:
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In how many ways can you arrange the word INDEPENDENCE such 17 Jul 2007, 22:59
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ajay_gmat
In how many ways can you arrange the word INDEPENDENCE such that the Ds and the Es are always together.. ??

Please solve :-D
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NNNCIP can be arranged in 4! ways

DDEEEE can be arranged in 5! ways

DEEEED can be arranged in 4! ways

4!(5!)(4!)

what is the oa? unsure here.
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sumande
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In how many ways can you arrange the word INDEPENDENCE such 17 Jul 2007, 23:08
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agree with dahcrap.

We have to consider all the Ds and Es together as one letter. Then we have total 7 letters which can be arranged in 7! ways.

However, there are 3 Ns here. So no. of ways = 7!/3!

Again, there are 2 Ds and 4 Es. These can be arranged in 6!/(2!*4!) ways.

Hence, total no. of words = (7!*6!)/(3!*2!*4!)
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Finding Perdition
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In how many ways can you arrange the word INDEPENDENCE such 18 Jul 2007, 02:55
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Ditto sumande, dahcrap.

I N D E P E N D E N C E

( DD EEEE) INPNNC

=>This can be arranged in 7!/3! ways (p(7,7)/(no of repetitions in this case of N).

Now we need to see how DD EEEE are arranged.
=> This can be arranged as p(6,6)/2!4!

=> Multiplying we have 7!.6!/3!4!2!



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