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

Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Expert Answer:

For a odd number, we must have 1,3 or 5 at the unit's place.  So there are 3 ways of filling the unit's place.

 

1)     Since the repetition of digits is not allowed, the ten's place can be filled with any of the remaining 5 digits in 5 ways.  Now, four digits are left. So hundred's place can be filled in 4 ways.

 

So the required numbers = 3 x 5 x 4 = 60

 

2)     Since the repetition of digits is allowed, so each of the ten's and hundred's place can be filled in 6 ways.

 

Hence, required numbers = 3 x 6 x 6 = 108

Answered by  | 4th Jun, 2014, 03:23: PM