Q3 of 68 Page 346

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.


More from this chapter

All 68 →
1

Out of 12 consonants and 5 vowels, how many words, each containing 3 consonants and 2 vowels, can be formed?

 2

How many words, each of 3 vowels and 2 consonants, can be formed from the letters of the word ‘INVOLUTE’?

 4

In how many ways can 4 girls and 3 boys be seated in a row so that no two boys are together?

 5

How many words, with or without meaning, can be formed from the letters of the word, ‘MONDAY’, assuming that no letter is repeated, if (i) 4 letters are used at a time? (ii) all letters are used at a time? (iii) all letters are used, but the first letter is a vowel?