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# How many arrangements are possible with the letters of the

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Re: How many arrangements are possible with the letters of the [#permalink]
souvonik2k wrote:
How many arrangements are possible with the letters of the word 'PROFILE', if no two consonants are to come together?

A) 36
B) 120
C) 144
D) 288
E) 576

Here we have 3 vowels (O,I,E) and 4 consonants (P,R,F,L). Since no 2 consonants are to come together, the positions of consonants are * and vowels are _ as following: *_*_*_*.
We have 4! ways to arrange 4 consonants into 4 positions and 3! ways to arrange 3 vowels into 3 positions.
Consequently there are 4!*3!=144 arrangements.
Re: How many arrangements are possible with the letters of the [#permalink]
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