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.
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.
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
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