Q. 3 A5.0( 2 Votes )

# How many words, with or without meaning can be formed from the letters of the word ‘MONDAY’, assuming that no letter is repeated, if

4 letters are used at a time

Answer :

Given that we need to find the no. of words formed by 4 letters which were taken from word ‘MONDAY.’

Let us find the no. of ways of choosing 4 letters and assume it to be N_{1}.

⇒ N_{1} = (No. of ways of choosing 4 letters from MONDAY)

⇒ N_{1} = (^{6}C_{4})

We know that ,

And also n! = (n)(n – 1)......2.1

⇒

⇒

⇒

⇒ N_{1} = 15

Now we need to find the no. of words that can be formed by 4 letters.

Now we need to arrange the chosen 4 letters. Since 1 person 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 4!.

Let us the total no. of words formed be N.

⇒ N = N_{1} × 4!

⇒ N = 15 × 24

⇒ N = 360

∴ The no. of words that can be formed by 4 letters of MONDAY is 360.

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