the LARGEST the sum can be is if n is randomly selected

everytime

The sum is then n^2

THe probablitity that this happens is (1/n)^n = 1/(n^n)

There are (n choose k) ways to arrange the terms.

So the total probablity is (n choose k)/(n^n)

Monica D.

asked • 09/06/19A sequence of numbers X_{1}, X_{2},... are produced by taking a random number from the set {1,2,3...n}.

The summation S_{k} is defined to be X_{1}+X_{2}+...+X_{k}.

Which of the following is a correct expression for the probability that S_{k} can be smaller or equal to n?

The answer is (nCk)/n^{n}

Why? __Explain__

Thank you in advance! My teacher gave this to me for math extension 1 & I’m so confused, I don’t even know where to begin with this question!

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the LARGEST the sum can be is if n is randomly selected

everytime

The sum is then n^2

THe probablitity that this happens is (1/n)^n = 1/(n^n)

There are (n choose k) ways to arrange the terms.

So the total probablity is (n choose k)/(n^n)

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