Question

How many three-digit odd numbers can be formed by using the digits 0, 1, 2, 3, 4, 5 if 

(i) The repetition of digits is not allowed

(ii) The repetition of digits is allowed

Answer 1

(i) The repetition of digits is not allowed 

The given digits are 0, 1, 2, 3, 4, 5. Here the odd number are 1, 3, 5. 

So the unit place can be filled in 3 ways (using the 3 odd number) 

After filling the unit place since 0 is a given digit be fill the 100’s place which can be filled in

Then the 10’s place can be filled in (6 – 2) 4 ways. 

So the number of 3 digit odd numbers = 3 × 4 × 4 = 48

(ii) The unit place can be filled in 3 ways. We are given 6 digits. 

So 10’s place can be filled in 6 ways and the 100’s place can be filled in (6 – 1) (excluding zero) 5 ways 

So the Number of 3 digit numbers = 3 × 6 × 5 = 90