Calculating the Probability of Getting k Heads from Flipping a Fair Coin n Times

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Homework Statement

If I flip a fair coin n times, that is the probability that I get k heads?

Homework Equations

nCk: the combination in which order doesn't matter s.t one picks k from n.

The Attempt at a Solution

there are 2*2*2*2*2...*2=2^n total outcomes. but the event specifies k ways of picking heads out of n flips. So, (nCk)/(2^(n)). Is this correct? Intuitively, I think its sound.
 
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Yes, it's quite sound.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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