MANAGEMENT

parallel_chase · Posted: Wed Jul 23, 2008 8:52 am Post subject: MANAGEMENT

In how many ways the letters of the word MANAGEMENT can be arranged with vowels in even positions.

OA coming after few discussions.

pepeprepa · Posted: Wed Jul 23, 2008 9:09 am Post subject:

I have 5400

egybs · Posted: Wed Jul 23, 2008 9:19 am Post subject: Re: MANAGEMENT

parallel_chase · Posted: Wed Jul 23, 2008 9:58 am Post subject:

There are 4 consonants and 2 vowels. The vowels are in repetition twice.

Vowels can be arranged in 5 even positions = 4! * 5C4

Remaining 6 positions can can be filled in 6! ways

M A E N repeated twice.

5!*6!/ (2!*2!*2!*2!) = 5400.

Thanks for the discussions

sudhir3127 · Posted: Wed Jul 23, 2008 10:16 am Post subject:

thanks parallel,,,

was just wondering that there are only 4 vowels ( AA EE)
they can arrange themselves 4 even places in 4p3 ways
5 consonants can arrange in 5 odd places in 5! ways
1 consonant can arrange itself in 1 even place in 6 ways

hence it shud be 4!*6!/2!*2!*2!*2!= 2160?

let me know where i am wrong?

pepeprepa · Posted: Wed Jul 23, 2008 12:10 pm Post subject:

(In your calculation, it is not 2160)
I think you forget that there are 5 even possible places.

sudhir3127 · Posted: Wed Jul 23, 2008 12:18 pm Post subject:

though there are 5 even places but only 4 vowels.. hence i used that one blank even place for 6 consonant as there are only 5 odd places for 6 consonants,,

pepeprepa · Posted: Wed Jul 23, 2008 2:03 pm Post subject:

I think you do not count all the different even places which can exist
Here are the vowel places.
_ X _ X _ X _ X _ X

(I dont write the consonants in the following examples it is useless)
I think you count only 1 out of 5 possibilities because of the place where there is no vowel: for example you only count AAEE_ but there are also AAE_E, AA_EE, A_AEE, _AAEE --> 5 way