6. Sixteen cards have been lost from a pack, which therefore contains only 36 cards. Two cards are drawn at random from the pack. The probability that both cards are red is \(\frac { 1 } { 3 }\).

1. Show that \(r\), the number of red cards in the pack, satisfies the equation $$r ( r - 1 ) = 420$$
2. Hence or otherwise find the value of \(r\).
3. Find the probability that, when three cards are drawn at random from the pack,
   1. at least two are red,
   2. the first one is red given that at least two are red.