Question

Use Pascal’s Triangle to determine the probability that you will get zero red lights (order does not matter) when looking at a row of five lights. Assume red and green are equally likely occurrences.

Answer 1

The 5th row of PT has 1 5 10 10 5 1
where the first number represents 5C0 or zero lights on out of 5
so P(zero lights) = 5C0/(1 + 5 + 10 + 10 + 5 + 1)
5C0 \(=\left(\begin{matrix}5 \\ 0\end{matrix}\right)\) (i.e. 5 choose 0)