Question

How many odd number of three digits each can be formed from the digit 2,4,6 and 7. if repetition of digits permitted?

Answer 1

I think it will be more than 1000

Answer 2

The answer to your question will vary according to a condition: If repetition of digits is allowed or not.

If allowed:

Let us consider the the 3rdposition first:

It can be filled with 3 possible digits given here- 1,3,5. So possible ways to fill the last place so that the number becomes odd is 3.

Now for the 2nd position:

It can be filled with all the provided digits i.e. in 7 possible ways.

Now for the 1st position:

It can be filled with all the provided digits but 0, hence total possible ways to fill the position is 6.

Hence total possible conditions of an odd 3 digit number under the given conditions with repetition being allowed would be 3.7.6 i.e. 126.

If not allowed:

Let us consider the 3rd position again:

It can be filled with 3 possible digits just like before i.e. by 1,3 or 5. So possible ways to fill the last place so that the number becomes odd is 3.(Say it is filled with 1)

Now let us take the 1st position into consideration:

It can be filled with digits excluding 0 (as it would make the number a 2 digit number) and also the digit that you placed on the 3rd position (i.e. 1), hence total possible ways to fill the position is 7–1–1= 5. (say it is filled with 6.)

Now for the 2nd position:

It can be filled with all the leftover digits as it will have no conditions. So possible digits are (0,2,3,4,5) i.e. number of possible digits that can be used is 5.

Hence total possible conditions of an odd 3 digit number under the given conditions with repetition not being allowed would be 3.5.5 i.e. 75.