Question

How many words, with or without meaning can be made form the letters of the word MONDAY, assumingthat 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 vowel?

Answer 1

Given work MONDAY has six different letters 

(i) When only 4 letters are to be used, then the number of words formed = 6 x 5 x 4 x 3 = 360 

(ii) When all letters are to be used, then the number of words formed = ⁶P₆ = 61 = 6 x 5 x 4 x 3 x 2 x 1 = 720 

(iii) In the given word, vowels are A, O

Since there are only two vowels A and O, therefore the first place can be filled in ²P₁ (2 ways) ways and the remaining 5 places can be filled from remaining 5 letters, in  ⁵P₅ ways. 

∴ Required number of words 

= ²P₁ x ⁵P₅ 

= 2 x 5! = 2 x (5 x 4 x 3 x 2 x 1) 

= 2 x 120 = 240