90 Ball Bingo

In the traditional game of bingo there are 90 balls and each player gets a card with 15 of those 90 balls on arrange in 3 lines of 5.

To match any five balls there are 3,003 combinations of matching the numbers (COMBIN(15,5)), only 3 of which result in a win line.

However, in my example we have different coloured balls in the game so the 90 are split as follows:

30 Blue
25 Yellow
18 Green
10 Red
7 Pink

Given this information I need to work out what the probability is of hitting a win line in each of the coloured balls (i.e. a "jackpot" line of all pink balls or all yellow balls etc) so it is possible to approximate the number of cards that will contain a "jackpot" win line.

So what proportion of cards purchased contain a line (or lines) of all the same colour?

Thanks to http://www.tips-for-excel.com for the prelimary Excel help! :tup: