A bag contains \(n\) beads. 7 of the beads are red and the rest are white. There are more white beads than red beads. Two beads are taken from the bag, at random, without replacement.
Complete the tree diagram.[3]
The probability that both beads taken are of the same colour is \(\dfrac{11}{18}\).
Show that \(n^2-37n+252=0\).[3]
By factorising \(n^2-37n+252=0\), find the values of \(n\).[2]
Explain why one of the solutions in part (c) must be rejected.[1]
Find, as a fraction in its simplest form, the probability that at least one of the two beads chosen is white in colour.[1]