SOLUTION: How many 5 letter word out of the first 8 letters in the english alphabet can be formed with the vowels always included? pls help with a little explanation.thanks a lot and more po

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Question 1057700: How many 5 letter word out of the first 8 letters in the english alphabet can be formed with the vowels always included? pls help with a little explanation.thanks a lot and more power.
Answer by solve_for_x(190) About Me  (Show Source):
You can put this solution on YOUR website!
There are two vowels in the first 8 letters of the alphabet (a and e). Since
these two letters must be included in every word, we must select 3 additional
letters from the remaining 6 consonants to get a group of 5 letters.

There are C%286%2C+3%29+=+6%21%2F%283%21%286+-+3%29%21%29+=+20 ways to do this, so there are
20 different five letter groups.

For each group, the five letters can be arranged in 5! = 120 ways.

The total number of "words" is then:

(120 words per group)(20 groups) = 2400 words