How many words, with or without meaning can be formed 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 ?

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Solution

(i) Total number of 4 letter words formed from the letters of the word 'MONDAY' is $=^{6} C_{4} \times 4! = 360$

(ii) Totalnumber of words formed by using all letters of the word 'MONDAY' is = 6! = 720

(iii) There are two vowels A and O. So, first place can be filled in 5! ways. So, total number of words beginning with a vowel $= 2 \times 5! = 240$

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