P and c

nikhilagrawal · Posted: Wed Jul 23, 2008 7:25 am Post subject: P and c

On how many ways can the letters of the word "COMPUTER" be arranged?

Vowels occupy the even positions.

pepeprepa · Posted: Wed Jul 23, 2008 7:33 am Post subject:

Any proposals?

sudhir3127 · Posted: Wed Jul 23, 2008 7:48 am Post subject:

My Answer is 2880...

4 even places to arrange 3 vowels hence 4P3 ways = 24
4 odd places to arrange 4 consonants - 4! = 24
1 even place to put 1 consonant= 5

hence 24 *24*5 = 2880

P_mashru · Posted: Wed Jul 23, 2008 8:12 am Post subject:

two possible approach

1 )
5 3 5 3..... = 60

5 consonets to fill first place in 8 alphabet word
3 wovels to fill 2nd place in 8 alphabet word

process repition for 4 times and answer 60

2 )
5 consonets to fill 4 odd positions = 5P4 = 120
3 vowels to fill 4 even positions = 4P3 = 24
1 consonent to fill 1 position remaining from vovel = 1

120 x 24 = 2880
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P_mashru · Posted: Wed Jul 23, 2008 8:17 am Post subject:

Oh clicked!

My first approach is wrong.. it is not possible only. Ignore the same but need input on 2nd approach comparing that of with sudhir

pepeprepa · Posted: Wed Jul 23, 2008 8:20 am Post subject:

Agree with 2880

parallel_chase · Posted: Wed Jul 23, 2008 8:32 am Post subject:

I got the same answer. 2880. I did the same way as Sudhir.