How many 3 number combinations?

Answer 1

That depends on a few factors:

A) How many unique digits can go into each slot?

B) Can a number be repeated? (eg. is 112 invalid because the 1 is used twice?)

C) Does order matter? (eg. is 123 the same as 132)

Assuming n=10 digits and r=3 slots

If repeats are allowed, then we get 10 possible items in the first slot. Since repeats are allowed, we also have 10 in our second slot, and 10 in our third. We don't have to cancel any out because of their ordering.

10 * 10 * 10 = 1000 = 103 = nr

If repeats are not allowed (let's say we have a bag of 10 pieces, each with a number on it. Once you've used a piece, you can't use it again), we can put any of 10 digits in the first slot, any of the 9 remaining in the second slot, and any of the 8 remaining in the third slot:

10 * 9 * 8 = 720 = 10!/7! = n! / ( n - r )!

If order doesn't matter, you'll need to cancel out any combination that is already represented, and there are formulas for that, but explaining it here might be a bit beyond the scope of the question. You'll find a more detailed lesson in combinations and permutations here:

See link below for more lessons on combinations and permutations