1. ## Different odd numbers

Hey there. I need a little help.

The problem is:

How many different odd numbers with different digits between 1000 and 10000 are there?

Thanks.

2. ## Re: Different odd numbers

Originally Posted by Breh
How many different odd numbers with different digits between 1000 and 10000 are there?
1) How many integers are there between $0~\&~10~?$ How many are odd?

2) How many integers are there between $10~\&~10^2~?$ How many are odd?

3) How many integers are there between $10^2~\&~10^3~?$ How many are odd?

YOU must post the answers to those three questions if you want more help.

3. ## Re: Different odd numbers

Originally Posted by Plato
1) How many integers are there between $0~\&~10~?$ How many are odd?

2) How many integers are there between $10~\&~10^2~?$ How many are odd?

3) How many integers are there between $10^2~\&~10^3~?$ How many are odd?

YOU must post the answers to those three questions if you want more help.
I think there's an easier way to go about this. Look at how many digits are available for the rightmost digit. Then for the leftmost. Then for the other 2.
Multiply all these together.

4. ## Re: Different odd numbers

Originally Posted by Breh
Hey there. I need a little help.

The problem is:

How many different odd numbers with different digits between 1000 and 10000 are there?
What exactly do you mean by "different digits"? I assume you mean that "3333" would not be included but do you mean all digits must be different? That is, would 3231 be included or not?

Thanks.

5. ## Re: Different odd numbers

Originally Posted by Breh
Hey there. I need a little help.

The problem is:

How many different odd numbers with different digits between 1000 and 10000 are there?

Thanks.
"different digits" does this mean 1001 is not included but 1023 is ?

6. ## Re: Different odd numbers

Originally Posted by Idea
"different digits" does this mean 1001 is not included but 1023 is ?
Moreover, do we count $3271~\&~7123~?$ They are different odd numbers, but they both have the same digits.

7. ## Re: Different odd numbers

Yes! We do count both of them, the value is different.

Exactly.

9. ## Re: Different odd numbers

my take on it is that it is all numbers

$d_3 d_2 d_1 d_0,~\ni (d_0 \in \{1,3,5,7,9\}) \wedge (d_j \neq d_k,~\forall j, k \in \{0,1,2,3\})$

clearly there are 5 possible selections for $d_0$

a little thought shows there are 8 possible selections for $d_3$

I leave it to OP to figure out how many selections are possible for $d_1,~d_2$ and to carry out the multiplication

10. ## Re: Different odd numbers

There are n cases:
1 : 1023
2 : 1025
.....
n-1:9873
n : 9875

11. ## Re: Different odd numbers

Originally Posted by Breh
How many different odd numbers with different digits between 1000 and 10000 are there?
Now we know that we are counting all four digit odd integers which have no digit appearing more than once.

$\_\_\_\_~\_\_\_\_~\_\_\_\_~\_\_\_\_~$ there are five choices for the last blank; then there are eight choices for the first blank; then eight times seven ways to fill the other two blanks. SEE HERE