How many words, with or without meaning, can be formed from the letter

1.	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?
Answer» 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. (ii) Now all the letters are used. Therefore, the number of words can be formed is = 6! = 720 (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.

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?

Answer»

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.

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

(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.