SOLUTION: There are ten lottery tickets, two of which are winners. Find the probability that in a sample of 6 tickets there will be no more than one winning ticket.

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Question 370130: There are ten lottery tickets, two of which are winners. Find the probability that in a sample of 6 tickets there will be no more than one winning ticket.

Found 2 solutions by edjones, spacesurfer:
Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website!
nCr=combinayion of n things taken r at a time.
((8C5 * 2C1)+(8C6))/10C6
=((56*2)+28)/210
=2/3 the probability that in a sample of 6 tickets there will be no more than one winning ticket.
.
Ed

Answer by spacesurfer(12) (Show Source):
You can put this solution on YOUR website!
First, there are a total of 210 ways to choose 6 tickets out of 10. That's 10 choose 6 = 210.
If there are 0 winners, then there are 8 tickets to choose from that are not winners (that's 10 total tickets - 2 winning tickets = 8 non-winners). So that means 8 choose 6 = 28 ways you can choose 6 tickets from 8 non-winning tickets where 0 are winners.
If there is 1 winner, then there you have 5 left for a non-winner. Hence, 8 choose 5 = 56. But there are 2 winners to choose from, so that's 2 x 56 = 112 ways 1 is a winner that 5 non-winners. Think of this this way: 2 winners to choose from x 56 ways to choose 5 out of 8 non-winners. Hence, it's 2 x (8 choose 5) - 112.
Add up 0 winners or 1 winner and you get 28 + 112 = 140.
Total possibilities = 210. So 140/210 = 2/3.