## Challenge 325: A Counter Challenge

A bag contains 7 counters which are identical except for their colour.

(i) If I draw out three counters at random, the probability that they are all the same colour is 2/35. How many different colours of counter are there in the bag? How many of each? How do you know?

An eighth counter is added to the bag. It is equally likely to be any of the colours that are already in the bag.

(ii) What is the probability of drawing three counters which are all the same colour now?