My question: Consider the numbers $1,2,3 ...,n$. All combinations of five of these numbers are written, and one combination is chosen at random. If the probability that this chosen combination does not contain the number $7$ is $0.875$, determine the value of $n$.
My problem: What should I do and how should I lay this problem out (all I can think of is a simple tree diagram?)? How do I create an equation where I can make $n$ the subject?
The most I can do: Is it saying there are $n! ,n! ,n! ,n! ,n!$? So choosing $1$ out of $5$ would be $1/5$. In $1/5$, I have the probability of not containing $7$ $(7/8)$ and $7$ $(1/8)$.