How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if.
(i) 4 letters are used at a time,
(ii) all letters are used at a time,
(iii) all letters are used but first letter is a vowel?

Solution:

The total no. of letters in the word MONDAY = 6 = n.

We know that the number of ways of selecting and arranging r different things from n different things is a permutation and we calculate it using the nPr formula.

(i) Number of 4-letter words that can be formed from the letters of the word MONDAY, without repetition of letters
= ⁶P₄
= 6!/(6 - 4)!
= 6!/2!
= 360.

(ii) Number of words that can be formed from the letters of the word MONDAY, if all letters are used at a time
= ⁶P₆ 
= 6!/(6 - 6)!
= 6!/0!
= 720. 

(iii) Number of words that can be formed from the letters of the word MONDAY, if all letters are used but the first letter is a vowel
= 2 × 5 × 4 × 3 × 2 × 1
= 240

NCERT Solutions Class 11 Maths Chapter 7 Exercise 7.3 Question 9

How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if. (i) 4 letters are used at a time, (ii) all letters are used at a time, (iii) all letters are used but first letter is a vowel?

Summary:

(i) Number of 4-letter words that can be formed from the letters of the word MONDAY without repetition of letters is 360.

(ii) Number of words that can be formed from the letters of the word MONDAY if all letters are used at a time 720.

(iii) Number of words that can be formed from the letters of the word MONDAY if all letters are used but the first letter is a vowel are, 240.