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Question

Let C be a set of 6 consonants {b,c,d,f,g,h} and V be the set of 5 vowels {a,e,i,o,u} and W be the set of seven-letter words that can be formed with these 11 letters using both the following rules.
(a) The vowels and consonants in the word must alternate.
(b) No letter can be used more than once in a single word.

If the number of words in the set W is 10K, then K is

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Solution

Consonants {b,c,d,f,g,h}
Vowels {a,e,i,o,u}
× × × ×
Case I: If word begins with consonants, then
Number of words =(6C4×4!)×(5C3×3!)
=360×60=21600

Case II: If word begins with vowels, then
Number of words =(5C4×4!)×(6C3×3!)
=120×120=14400

Total count =21600+14400=36000
10k=36000
k=3600

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