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by sportcntr3 » Wed Apr 22, 2009 10:03 am
In how many different ways can the letters of the word, 'EXPLAIN' be arranged so that, the vowels may occupy only the odd position?

a) 120
b) 250
c) 200
d) 500
e) 576

OA: 576
Last edited by sportcntr3 on Wed Apr 22, 2009 11:07 am, edited 1 time in total.
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by scoobydooby » Wed Apr 22, 2009 10:17 am
three vowels E, A, I can be arranged in 4 positions (1st, 3rd, 5th, 7th) in 4P3 ways. 4P3=4!=24 ways.

the 4 consonants (X, P, L, N) can be arranged in the remaining 3 slots (2nd, 4th, 6th) in 4P3 or 24 ways

or total number of ways in which the word can be arranged in 24*24=576 ways.

hence, E
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