SOLUTION: A box contains 20 blocks. Fifteen of the blocks are red, the rest are green. If six blocks are selected at random, how many ways can six red blocks be selected? I have tried 20P

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Question 727248: A box contains 20 blocks. Fifteen of the blocks are red, the rest are green. If six blocks are selected at random, how many ways can six red blocks be selected?
I have tried 20P6 but I am not sure that is the right formula to be using. I figure some sort of probability of red vs. green needs to be included.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Order does NOT matter, so you do NOT use n P r (permutation), you use n C r (combination)

So there are 15 C 6 = 5005 distinct ways to pick 6 red blocks

This is out of 20 C 6 = 38760 ways total (to pick any color block and pick 6 of them)

So the probability of picking 6 red blocks is

P(6 red blocks) = (# of ways to pick 6 red blocks)/(# of ways to pick 6 blocks)

P(6 red blocks) = (15 C 6)/(20 C 6)

P(6 red blocks) = (5005)/(38760)

P(6 red blocks) = 0.12912796697627