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

(i) There are total 6 letters in the word 'MONDAY'.
Total number of words using 4 letters at a tiome = `.^(6)P_(4)`
`= (6!)/(2!) = (720)/(2) = 360`
(ii) No. of words using all 6 letters at a time
`= .^(6)P_(6) = (6!)/(0!) = (720)/(1) = 720`
(iii) If first letter is a vowel, then no. of ways of filling first letter `= 2 (O` or A)
No. of ways of filling remaining 5 letters `= 5! = 120`
Therefore, total words `= 2 xx 120 = 240`