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?
There are 5 vowels and 21 consonants in English alphabets.
Choosing two vowels out of 5 would be done in 5C2 ways
Choosing 2 consonants out of 21 can be done in 21C2 ways
The total number of ways selecting 2 vowels and 2 consonants
= 5C2 × 21C2
Each of these four letters can be arranged in four ways 4P4
Total numbers of words that can be formed are
24 × 2100 = 50400
6