document.write( "Question 655222: 5 names need to be drawn from a pool of 10 and they are done so by putting them in a bag and using a blind draw. My question is - are the chances the same whether the blind draw is one name at a time, until 5 have been drawn, or drawing all 5 at once. It doesn't seem like it should matter either way, yet the first way (one at a time) also appears to give the first name a 10% chance, the second one a 11.1% chance (1/9), the third one a 12.5% chance (1/8) and so on until the fifth and final name has a 16.7% chance, which is a bit higher than the first one at only 10%. I'm confused! \n" ); document.write( "
Algebra.Com's Answer #409104 by stanbon(75887)\"\" \"About 
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5 names need to be drawn from a pool of 10 and they are done so by putting them in a bag and using a blind draw.
\n" ); document.write( "My question is - are the chances the same whether the blind draw is one name at a time, until 5 have been drawn, or drawing all 5 at once.
\n" ); document.write( "----
\n" ); document.write( "5 at a time:
\n" ); document.write( "# of possible outcomes: 10C5 = 252 unique groups of 5 names
\n" ); document.write( "# of ways to win: 1 group of 5 names
\n" ); document.write( "P(choose correct 5 from 10) = 1/10C5 = 1/252 = 0.003968...
\n" ); document.write( "------
\n" ); document.write( "One at a time:
\n" ); document.write( "1st good: 5/10
\n" ); document.write( "2nd good: 4/9
\n" ); document.write( "3rd good: 3/8
\n" ); document.write( "4th good: 2/7
\n" ); document.write( "5th good: 1/6
\n" ); document.write( "P(5 correct names) = (5*4*3*2*1)/(10*9*8*7*6) = 1/10C5 = 0.003969...\r
\n" ); document.write( "\n" ); document.write( "----
\n" ); document.write( "The results are the same.
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "
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