168. The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet? 

Number of consonants = 21
                 Number of vowels = 5
A word contains two vowels and two consonants will be formed as
(i)  select 2 vowels out of 5
(ii)  select 2 consonants out of 21
(iii) arrange 2 + 2 = 4 letters to obtain different words
(iv) use fundamental principle of counting.
          (i) Number of ways in which 2 vowels can be selected out of 5 = 
          (ii) Number of ways in which 2 consonants can be selected out of 21 = 
           (iii) Number of permutations (to form different words) of the four letters = 4!
Hence, by fundamental principle of counting, the number of words formed.

                               
                                = 10 x 210 x 24 = 50400