Answer :

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.


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