SOLUTION: consider words of length 10 which only contain letters from the set {a,e,i,o,u,r,s,t,v,w}, suppose repetition of letters is not allowed. 1. how many different words of length 10 a

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Question 775364: consider words of length 10 which only contain letters from the set {a,e,i,o,u,r,s,t,v,w}, suppose repetition of letters is not allowed.
1. how many different words of length 10 are there?
2. how many different words of length 10 are there if the consonants i.e. r,s,t,v,w and the vowels i,e, a,e,i ,o, u must alternate
3. how many different words of length 10 are there if all five vowels must be adjacent in each word?
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
consider words of length 10 which only contain letters from the set {a,e,i,o,u,r,s,t,v,w}, suppose repetition of letters is not allowed.
1. how many different words of length 10 are there?
10! = 3628800

2. how many different words of length 10 are there if the consonants i.e. r,s,t,v,w and the vowels i,e, a,e,i ,o, u must alternate
They can be CVCVCVCVCV or VCVCVCVCVC [C=consonant, V=vowel]

For each of those 2 types, there are 5! ways to arrange the consonants
and 5! ways to arrange the vowels:

5!5!2 = 1201202 - 28800

3. how many different words of length 10 are there if all five vowels must be adjacent in each word?
VVVVVCCCCC, CVVVVVCCCC, CCVVVVVCCC, CCCVVVVVCC, CCCCVVVVVC, CCCCCVVVVV

For each of these 6 types, there are 5! ways to place the consonants and 5!
ways to arrange the vowels:

5!5!6 = 1201206 - 86400

Edwin
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