1. [SOLVED] probability sampling

When I open a bank account i am allocated a 4 digit personal identification number(which may begin with one or more zeros) at random with all possibilites equally likely. Find the probability that:

The digits im my number are in strictly increaing order.

Thanks

2. If we take any selection of four digits, ex. (4,9,4,8), we can always arrange the four is ascending order: (4,4,8,9). Thus, all we need to finish is to determine how many possible four-selections are there.
$\displaystyle { {4+10-1} \choose 4}$ and there are $\displaystyle 10^4$ possible pin numbers.

3. Originally Posted by Plato
If we take any selection of four digits, ex. (4,9,4,8), we can always arrange the four is ascending order: (4,4,8,9). Thus, all we need to finish is to determine how many possible four-selections are there.
$\displaystyle { {4+10-1} \choose 4}$ and there are $\displaystyle 10^4$ possible pin numbers.
I understand that there are 10^4 possible pin numbers but i do not understand what means.

can you please clarify what you mean by this.

I thought the the answers was:

10! / (4!(10-4)!))/10 ^ 4

which is equall to 210/10 ^ 4

thanks

4. That is the selection formula: $\displaystyle { {K+N-1} \choose K}$, $\displaystyle { {M} \choose J}=\frac {M!}{(M-J)!(J!)}$ .

If we have N difference types of items from which we are to select K items, we may pick more than one of any type.
For example you are to pick four pieces of fruit from apples, oranges, or bananas.
You may pick two apples and two bananas.

5. Thanks once again for helpping me.