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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.
I. The vowels and consonants in the word must alternate.
II. No letter can be used more than once in a single word.

Then the number of words in the set W is

A
32000
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B
36000
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C
42000
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D
38000
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Solution

The correct option is B 36000
Consonants {b,c,d,f,g,h}
Vowels {a,e,i,o,u}
× × × ×
Case 1: If the word begins with a consonant, then
Number of words =(6C4×4!)×(5C3×3!)
=360×60=21600

Case 2: If the word begins with a vowel, then
Number of words =(5C4×4!)×(6C3×3!)
=120×120=14400

The number of words in set W equals 21600+14400=36000

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