document.write( "Question 371108: There are ten raffle 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. I am more concerned with how to find the answer then I am with what the actual answer is. Can you please explain. Thanks.
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Algebra.Com's Answer #313531 by spacesurfer(12) $\"\"$ $\"About$

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The solution provided by the first solver is wrong. I just solved this problem for another student and the answer is 2/3.\r
\n" ); document.write( "\n" ); document.write( "Here's the solution.\r
\n" ); document.write( "\n" ); document.write( "First, there are a total of 210 ways to choose 6 tickets out of 10. That's 10 choose 6 = 210.\r
\n" ); document.write( "\n" ); document.write( "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.\r
\n" ); document.write( "\n" ); document.write( "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.\r
\n" ); document.write( "\n" ); document.write( "Add up 0 winners or 1 winner and you get 28 + 112 = 140.\r
\n" ); document.write( "\n" ); document.write( "Total possibilities = 210. So 140/210 = 2/3. \n" ); document.write( "

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