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 N1.
⇒ N1 = (No. of ways of choosing 4 letters from MONDAY)
⇒ N1 = (6C4)
We know that 
,
And also n! = (n)(n – 1)......2.1
⇒ 
⇒ 
⇒ 
⇒ N1 = 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 = N1 × 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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