The English alphabet has 21 consonants and 5 vowels. How many words wi

1.	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?
Answer» 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.

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?

Answer»

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.