Probability of System Malfunction & Defective Tubes Selection

axnman
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Que. 1 : In a mech. sys. 5 bulbs are used and system will operate if any 3 are functioning. Given that 15% of bulbs are defective , with aid of binomial PDF determine what are the chances that the system will malfunction?

Que. 2 :
Suppose 15% of total population of tubes is defective and that 5 tubes are randomly selected. Determine the probability that there will be among those selected:
1) no defectives
2) only 2 defectives
3) no more than 2 defectives
4) only 3 defectives
5) no more than 3 defectives
 
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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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