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

Explanation

2 vowels can be chosen in ` ^5 C_2` ways

2 consonants can be chosen in ` ^21 C_2` ways

Thus four letters can be arranged in ` ^4 P_4` ways

If .n. is the number of words, then
``
n= ^5 C_2 xx ^21 C_2 xx ^4 P_4=5 !/2 ! 3 ! xx 21 !/2 ! 19 ! xx 4 !=50400
``