A group of \(N\) children are at school celebrating National Day. The children come in either red or white T-shirts. Three girls from the group wore white T-shirts.
Two children are selected at random from the group. The probability that both are girls wearing white T-shirts is \(\dfrac{1}{70}\). Find \(N\).[2]
One child is selected at random. The probability that it is a girl wearing a red T-shirt is \(\dfrac37\). Three children are chosen at random. The probability that one is a boy wearing a white T-shirt and two are girls wearing red T-shirts is \(\dfrac{108}{665}\). Find the value of \(a\), of \(b\) and of \(c\) as shown in the table of information about the group of children.[3]
| White T-shirts | Red T-shirts |
|---|
| Boys | \(a\) | \(b\) |
| Girls | \(3\) | \(c\) |