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 leters 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

There are 6 letters in the word MONDAY. So, the total number of words is equal to the number of arrangements of these letters taken four at a time
The number of such arrangements `= .^(6)P_(4)=(6!)/((6-4)!)=(6!)/(2!)=(6.5.4.3.2.1)/(2.1)=360`
Hence, total number of words = 360
(ii) Total number of arrangements in this case `= .^(6)P_(6)= 6! =720`
(iii) Total number of arrangements when all letters are used but the first lette is a vowel
`=2.^(5)P_(5)=2.5!=2xx5xx4xx3xx2xx1=240`