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Simple S1 Probability question

If anyone could give me a hand with this, that'd be great.

A bag contains 30 platic tiles which are used in a word game. Each tile has a single letter written on it. 12 of the tiles have vowels written on the, and the remaining 18 tiles have consonants written on them. A contestant in the game picks 7 tiles at random, without replacement

i)Find the probability that, of the 7 tiles, 4 have vowels written on them and 3 have consonants written on them.

So far I have worked out (12*11*10*9)*(18*17*16)/(30*29*28*27*26*25*24) = 0.00567 (3 s.f.); however, I think that there should be something to take into account the fact that it doesn't matter which order the tiles are picked in?

Once again, thanks for any help.

Reply 1

jr2007

I think you need to work out the probabilities of each combination of getting to having 7 tiles with 4 vowels and 3 consonants and add em. I think its something like AND rule for each probability and OR rule for the total probability.

Probably a way to do it quicker but thats what I think would help. Try like a tree diagram