SOLUTION: From seven consonants and five vowels, how many six letter words can be formed consisting of 3 different consonants and three different vowels? The words need not have meanin

First we find the number of vowel-consonant placements 
for instance, whether CVVCCV or VCVCVC or VVCVCC, etc.

There are 6C3*3C3 = 20 ways to choose position for the
consonants (C's) and vowels (V's)  

For each of these 20 ways, there 21P3 = 7980 ways to 
place consonants in those three positions with C's.

That's 20(7980) = 159600 ways.

For each of those 159600 ways, there are 5P3 = 60 ways to
place vowels in those three positions with V's.

That's 6C3*3C3*21P3*5P3 = 20*1*7980*60 =  9576000 ways.

Edwin