How many different three-digit numbers can I make with three 3s, two 2s, and one 1? I'd like to use actual calculations instead of just counting them all.
What I am curious about is how am I supposed to do this kind of problem when the numbers are more complicated? For example, "How many different five-digit numbers are available with x threes, y twos, and z ones?"
After analyzing some data using this pattern, I have discovered that if the amount of different numbers (example: four 4s, three 3s, two 2s, and one 1 would be 5 different numbers) would be n, you would use this equation (n is a positive integer greater than or equal to the amount of digits(3 in this equation)):
p = (n - 1)(n - 1) + ((n - 1)(n(n) - 2) + (n - 2))
(p means the possibilities)
Tell me if you found a simpler way of writing this.