The English alphabet has 21 consonants and 5 vowels. How many words with two different consonants and three different vowels can be formed from the alphabet?
2 consonants out of 21 consonants can be chosen in 21C2 ways. 3 vowels out of 5 vowels can be chosen in 5C3 ways. Length of the word is = (2 + 3) = 5 And also 5 letters can be written in 5! Ways. Therefore, the number of words can be formed is = (21C2 X 5C3 X 5!) = 252000.