There are 6 orange sweets in a bag of n sweets. Hannah picks two sweets at random without replacement, and they are both orange. Show that n^2-n-90=0

This is a multi step question that requires both good understanding of probability and maniuplating algebraic fractions.PROBABILITYThe first step is recognizing that as there are 6 orange sweets out of a total n, the probability of picking an orange sweet once is 6/n. (For example, if n=12, we would pick an orange sweet 6 times out of 12 on average, so we would have the probability =6/12, or one half)Then, notice we now have 5 orange sweets in a bag of n-1 sweets. So the probability of picking an orange sweet on the second go is 5/n-1 (in our example this happens 5 times out of 12-1=11). Most importantly, we have to remember than when we have two (independant) events, the probability of them both happening is their probabilities multiplied together. In this case, the probability of picking an orange sweet on the first and second go is (6/n)(5/n), and we know this equals 1/3. ALGEBRA(6/n)(5/n-1)=1/3 multiply tops and bottoms of fractions together(65/n(n-1))=1/3 multiply out denominators (imagine moving them from the bottom of the fraction to the other side)653=1n(n-1) expand brackets 90= n^2-n subtract 90 n^2-n-90=0