Question 1082667
<pre><b>
Set of vowels in "QUESTION" = {U,E,I,O}
Set of consonants in "QUESTION" = {Q,S,T,N}
<i>
Choose the 2 vowels:
</i>
4 vowels Choose 2 = 4C2 = (4*3)/(2*1) = 6 ways.
<i>
Choose the 2 consonants:
</i>
4 consonants Choose 2 = 4C2 = (4*3)/(2*1) = 6 ways.
<i>
Arrange them all possible ways:
</i>
The 4 letters can be arranged in 4P4 = 4! = 24 ways.

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

Edwin</pre>