# How many words, with or without meaning, can be formed from the letters of

Question:

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?

Solution:

There are 6 letters in the word ‘MONDAY’, and there is no letter repeating.

(i) 4 letters are used at first. 4 letters can sit in different ways. So, here permutation is to be used. So, the number of words that can be formed = 6P4 = 360. [Answer (i)]

(ii) Now all the letters are used. Therefore, the number of words can be formed is = 6! = 720 [Answer(ii)]

(iii) Now the first letter is a vowel. There are 2 vowels in the word ‘MONDAY’, ‘O’ and ‘A’. Let’s take ‘O’ as the first letter. Then we can place the 5 letters among the 5 places. So, taking ‘O’ as the first letter, a number of words can be formed is = 5! = 120. Similarly, taking ‘A’ as the first letter, a number of words can be formed = 5! = 120. So, the total number of words can be formed taking first letter a vowel is = (120 + 120) = 240. [Answer(iii)]