Question:
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?
Solution:
2 consonants out of 21 consonants can be chosen in ${ }^{21} C_{2}$ ways. 3 vowels out of 5 vowels can be chosen in ${ }^{5} C_{3}$ ways. Length of the word is $=(2+3)=5$ And also 5