Is there an equation that can derermine the number of possible
combinations for a lock given number of characters to choose from,
number of slots to fill, and whether or not you could have repeating
characters? Can I get an example with a 4 slot combo with digits 0-9
possible repeating, 3 slot combo with digits 1-60 possible repeating,
5 slot combo with two digits non repeating.

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Clarification of Question by zaaland-ga on 01 Dec 2005 08:21 PST

Noting googles anti-homework question policy, feel free to provide any
examples that include at least two differant types of combonation
locks. Tip if anybody can anwser this and find a way to put a cypher
lock into an equation as well.

If I understand your question correctly:

Imagine having a one slot lock with 0-9 digits, with repeating.  You'd
have 10 choices, yes?

Two slots...you'd have 10 for the first slot and 10 for the second
slot.  A systematic way of trying all the combinations would be to do
0 0, 0 1, 0 2,...1 0, 1 1, 1 2, etc...yielding 10x10 or 100
combinations.

Same deal with 3 slots...10x10x10 or 1000 combinations and 4 slots
10x10x10x10 or 10000 combinations.

For 3 slot combo with 1-60 possible repeating it's same deal as before
but you have 60 digits instead of 10.  Thus you have 60x60x60 or
216000 combinations.

I'm not sure I understand the last question...do you mean a 5 slot
lock with only two possible digits and those digits can't
repeat...like 0 1 0 1 0 would be ok, but 1 1 0 1 0 would not...or did
you forget to list the number of digits for the 5 slot lock...for
example 10 digits, where the same digit could not be used twice?

In the first case you'd have 2 choices for the first slot and only 1
choice for the other slots...2x1x1x1x1 or 2 choices...those choices
being 1 0 1 0 1 or 0 1 0 1 0.  In the second case (assuming 10 digits)
you'd have 10 choices for the first lock, 9 choices for the second, 8
for the third, 7 for the fourth, and 6 for the fifth giving you
10x9x8x7x6 or 30240 combinations.

I can figue them out like you did, I was wondering if there was a
quicker method.  My last example was flawed, I was trying to depict a
cypher lock in which you could only use any of the five push buttons
once, but I can't think of the correct way it should be described to
work in an equation.

Well the equation for the locks with repeating digits would be number
of digits to the power of number of slots.

So a slot 4 lock with 10 digits is 10 ^ 4 a 3 slot lock with 60 digits is 60 ^ 3.

If each digit can only be used once it would be number of digits
factorial divided by number of digits minus number of slots factorial.
 In the case of a slot 5 lock with 10 digits where each digit can be
used only once you get:

10!/(10-5)!

I follow you up untill this point
"If each digit can only be used once it would be number of digits
factorial divided by number of digits minus number of slots factorial.
In the case of a slot 5 lock with 10 digits where each digit can be
used only once you get:

10!/(10-5)!"
Maybe the exclaimations stand for something I don't understand, or
there's more to it, 10/(10-5)=2...?, Not the number I was expecting. 
Do you mean 10 ^ 10/(10-5), I'm not normally this dense but sometimes
it takes a while for things to sink in before I fully understand them.
Also my question is still whether or not you can write a no bull----
equation for this although you have been very helpfull so far.

They stand for factorial...5! is 5x4x3x2x1 or 120