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So the example I'm trying to complete is the following:

The English alphabet contains 21 consonants and five vowels. How many strings of six lowercase letters of the English alphabet contain:

a) exactly one vowel?

My first thought was that we pick a vowel: C(5,1) Then we pick 5 out of the 21 consonants: C(21,5) or is it 21^5 (the question doesn't state that we can't re-use consonants)

Afterwards we have to sort them into a string which I think would be P(6,6)

The result I get is way too high, the answer is supposed to be (according to the answers to odd numbers) 122,523,030.

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    In addition to joriki's nice answer, see: http://www.gvu.gatech.edu/~jarek/courses/1050/slides/X13Permutations.ppt2012-12-09

2 Answers 2