Math

Here's a chalenging one that i can't do at all.

A deck of cards has 6 yellow, 6 green, and 5 black cards. You pick four cards from the deck. Cards are not returned after they are picked.

What's the probability of picking-
first not green, second not green, third not black, fourth not gray.

Its really hard.
Plz Help

You never mentioned gray cards. Do you mean the fourth card picked is not green? If not, ANY card drawn in not gray.
For the first draw, the not-green probability is 11/17. If this happens, there are 10 not-green cards left out of 16, and the probability of the second card being not green is 10/16. Now there are 15 cards left and 6 are green, since none were drawn. The other nine are either
4 yellow and 5 black, or
5 yellow and 4 black, or
6 yellow and 3 black
The relative probabilities of these situations are 3/11, 6/11 and 2/11, respectively. (I will leave you to figure out why).
The probability of the third card being not black is:
(3/11)(10/15) + (6/11)(11/15) + (2/11)(12/15) = (30+66+24)/165 = 120/165 = 8/11
The overall probability is
(11/17)*(5/8)*(8/11)* 1= 5/17

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