Drawing Probablity Question

[Fisherman23]

OK so there are 60 cards in this deck. Seven cards will be selected at random. 4 of the 60 cards are the cards we want.

What is the probability of drawing one when selecting 7 random cards?

Probability of drawing two?

3?

All four?

[Fisherman23]

I think the first one would be:

[(4/60 x 55/59 x 54/58 x 53/57 x 52/56 x 51/55 x 50/54) x7] = 26.7%

[AaronBrown]

There are C(60,7) ways of drawing 7 cards from 60.

C(60,7) = C(56,7) + 4*C(56,6) + 6*C(56,5) + 4*C(56,4) + C(56,3)

The first term, C(56,7) is the number of ways to draw 7 cards without using any of the four. The second term, 4*C(56,6) is the number of ways to draw 7 cards using exactly one of the four. And so on.

That makes the probability of getting 0 60%, 1 34%, 2 6%, 3 0.38% and 4 0.007%.