# Math Help - permutation

1. ## permutation

the number of three letter words which can be formed from the word PROPOSAL in which the middle letter is a vowel is

how to make cases for this question

help

2. ## Re: permutation

Originally Posted by prasum
the number of three letter words which can be formed from the word PROPOSAL in which the middle letter is a vowel is

how to make cases for this question

help
a) with letter repetition :

$2 \cdot 6^2 = 72$

b) without letter repetition :

$2 \cdot \frac{5!}{(5-2)!}=40$

3. ## Re: permutation

40 words is not correct as I count. There are 11 sets of words beginning OA RA SA PA LA 00 RO SO PO LO AO.I count 22 words middle letter A and 31 words middle letter O