SOLUTION: If you were allowed to use a letter from the word "QUESTION" only once, how many 4-letter codes formed containing two vowels and two consonants?

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Question 1082667: If you were allowed to use a letter from the word "QUESTION" only once, how many 4-letter codes formed containing two vowels and two consonants?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

Set of vowels in "QUESTION" = {U,E,I,O}
Set of consonants in "QUESTION" = {Q,S,T,N}

Choose the 2 vowels:

4 vowels Choose 2 = 4C2 = (4*3)/(2*1) = 6 ways.

Choose the 2 consonants:

4 consonants Choose 2 = 4C2 = (4*3)/(2*1) = 6 ways.

Arrange them all possible ways:

The 4 letters can be arranged in 4P4 = 4! = 24 ways.

Answer: (4C2)(4C2)(4P4) = (6)(6)(4!) = (36)(24) = 864.

Edwin