# . 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?

Explanation:

The number of permutations of  different objects arranged  at a time - denoted as  is given by the following formula.

The total number of the alphabet in the word MONDAY is 6

So, n = 6

(i) Number of 4 letter words that can be formed from the letters of the word MONDAY, without repetition of letters, is given by the number of permutations of 6 different objects taken 4 at a time.

Thus, the required number of words that can be formed using 4 letters at a time is

Hence, the number of words that can be formed using 4 letters at a time is 360

(ii)  Number of words that can be formed by using all the letters of the word MONDAY at a time is the number of permutations of 6 different objects taken 6 at a time.

Thus, the required number of words that can be formed when all letters are used at a time is