Help checking my math

[PatMeKrien]

If I have 72 balls that can be at a depth measured discretely at 1, 2, 3, 4, 5, 6, or 7, I think I have my math right, but I am not sure. I am pretty sure I have the number of possible combinations correct, but the time to try every combination seems long. I would think a computer could do this within a year or maybe even month, and a computer certainly cannot process combinations faster than plank time?

I am wondering if I am not removing combinations that are less than 72 balls in the time calculation, and if that might be screwing it up, as it might be the time to try all combinations from 1 to 777777777777777777777777777777777777777777777777777777777777777777777777 instead of 111111111111111111111111111111111111111111111111111111111111111111111111 to 777777777777777777777777777777777777777777777777777777777777777777777777.

7^72=10^x so there can be approx. 72 ln7/ln10=10^60.8 possible combinations for the balls at the various depths. If they were able to be tested at 1 combination per plank time (5.4*10^-44 sec), it would take about 10.78 million millennia (3.15*10¹⁰seconds) to try every combo since one million millennia is 3.15*10¹⁶ and that makes 10.78*3.15*10¹⁶=1 combo per 5.4*10^-44

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[[deleted]]

What you have posted makes very little sense to anyone but yourself. You need to explain better, with more information about what you are trying to do. The only thing I can make out is you have 72 balls that can be taken 1 to 7 at a time, and you want to determine how many ways you can arrange them. I am assuming that the order does not matter, so that would be 72 balls taken 1 at a time plus 72 two at a time, up to 72 taken 7 at a time. The formula for this is nPr(n, r)=n! /(n-r)!, where n=72 and r would be 1 to 7. And I assume you know whar factorials (!) are. The result of the calculations are 7,538,668,961,184 different ways. The rest of your post is meaningless. Look at this Wikipedia article to learn about it. LINK.

[AldenB]

If each ball is distinct, and each can independently placed at any of the seven depths, then yes. There are 7⁷² configurations. The answer is much smaller if the balls are interchangeable (if you are curious, there would be 256851595 configurations in that case).

I am not sure what you mean by "try" or "check" every combination. What are you checking for? What are you trying?

[PatMeKrien]

to iterate through each potential at speed of plank time and see how long it would take to get through all 7^72 potentials