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# How many wo

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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