Question

How many letters words with or with out 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?

Answer 1

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 = 6P4 = 6/(6 - 4) = 6/2 = (6 x 5 x 4 x 3 x 2 x 1)/(2 x 1) = 360

Hence, total number of words = 360

(ii) Total number of arrangements in this case = 6P6 = 6! = 720

(iii) Total number of arrangements when all letters are used but the first letter is a vowel

= 2 × 5P5 = 2 × 5! = 2 × 5 × 4 × 3 × 2 × 1 = 240.