Question

How many three-digit odd numbers can be formed by using the digits 1, 2, 3, 4, 5, 6 if repetition of digits is not allowed?

(a) 72 

(b) 108 

(c) 40 

(d) 60

Answer 1

(d) 60

For a number to be odd, we should have 1 or 3 or 5 at the unit’s place. So there are 3 ways of filling the unit’s place. 

As repetition of digits is not allowed, the ten’s place can be filled in 5 ways with any of the remaining 5-digts and the hundred’s place can be filled in 4 ways by the remaining 4-digits. So, 

Required number of three-digit odd numbers = 3 × 5 × 4 = 60.