Question

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

Answer 1

No. of ways of selecting 2 vowels out of 5 vowels `= .^(5)C_(2)`.
No. of ways of selecting 2 consonants out of 21 consonants `= .^(21)C_(2)`.
No. of ways to arrange 2 vowels and 2 consonants i.e., 4 letters = 4!
Therefore total no. of words `= .^(5)C_(2) xx .^(21)C_(2) xx 4!`
`= (5 xx 4)/(2 xx 1) xx (21 xx 20)/(2 xx 1) xx 24`
`= 10 xx 210 xx 24`
`= 50400`