How to transform this word problem into a binomial distribution equation

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Homework Statement


Because not all airline passengers show up for their reserved seat, an airline sells 125 tickets for a flight that holds only 120 passengers. The probability that a passenger does not show up is 0.10, and the passengers behave independently

a) What is the probability that every passenger who shows up can take the flight?
b) What is the probability that the flight departs with empty seats?


Homework Equations



f(x) = n nCr x p^x(1 - p)^n-x

The Attempt at a Solution



a) 125 nCr 120 (0.9)^120*(0.1)^5

b) 125 nCr 0 (0.9)^0 * (0.1)^125
 
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let n be the number of passengers and p be the probability they won't turn up.
(a)find prob less than or equal to 5 don't turn up
(b)similar thing as (a)
 
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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