Question

Total number of three letter words that can be formed from the letters of the word ‘SAHARANPUR’ is equal to

(A)  210 

(B)  237 

(C)  247 

(D)  227

Answer 1

Correct option  (C) 247

The word ‘SAHARANPUR’ has 1S, 3A, 1H, 2R, 1N, 1P, 1U.

When all letters are different,

Corresponding ways =

⁷C₃ .3! = ⁷P₃ = 210

When two letters are of one kind and the other is different,

Corresponding ways = ²C₁.⁶C₁. 3!/2! = 36

When all letters are alike, corresponding ways = 1.

Thus, total number of words that can be formed is

210 + 36 + 1 = 247