How many words, with or without meaning can be formed from the letters of the word ‘MONDAY’, assuming that no letter is repeated, if
all letters are used but the first letter is a vowel?
Given that we need to find the no. of words formed by all letters from MONDAY in which the first letter should be a vowel.
In MONDAY the vowels are O and A. We need to choose one vowel from these 2 vowels for the first place of the word.
Let us find the no. of ways of choosing vowel and assume it to be N1.
⇒ N1 = (No. of ways of choosing a vowel from 2 vowels)
⇒ N1 = (2C1)
We know that 
,
And also n! = (n)(n – 1)......2.1
⇒ 
⇒ 
⇒ 
⇒ N1 = 2
Now we need to find the no. of words that can be formed by remaining 5 letters.
Now we need to arrange the remaining 5 letters. Since every letter differs from other. The arrangement is similar to that of arranging n people in n places which are n! ways to arrange. So, the total no. of words that can be formed is 5!.
Let us the total no. of words formed be N.
⇒ N = N1 × 5!
⇒ N = 2 × 120
⇒ N = 240
∴ The no. of words that can be formed by all letters of MONDAY in which the first letter is a vowel is 240.