What is the probability that having $n$ random numbers (each maximum $n$-bit - numbers can be repeated) there is a sum of up to $2^n$ (the sum of any number of numbers - minimum one number, maximum $n$ numbers)?
2026-04-13 12:06:31.1776081991
What is the probability that having $n$ random numbers (each maximum $n$-bit - numbers can be repeated) there is a sum of up to $2^n$?
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Hint: You can use stars and bars to find the number of ordered ways to express $2^n$ as a sum of $k$ terms. How many ordered choices of $n$ numbers are there? Take the ratio.