bonanova Posted November 29, 2014 Report Share Posted November 29, 2014 Someone is willing to bet, at even odds, that if he throws six fair dice, exactly four distinct numbers will show. For example 3 3 4 4 5 6 or 3 3 3 4 5 6. Do you take the bet? Quote Link to comment Share on other sites More sharing options...
0 witzar Posted November 30, 2014 Report Share Posted November 30, 2014 There are two ways to get exactly four numbers: aaabcd and aabbcd. First you can get in 6_choose_3*6*5*4*3 ways, and second you can get in 6_choose_4*3*6*5*4*3 ways, making total of (6_choose_3+6_choose_4*3)*6*5*4*3 = (20+15*3)*6*5*4*3 = 23400 ways. We should not accept the bet if 23400/6^6 > 1/2. It's close, but we are slight underdog, so we reject. Quote Link to comment Share on other sites More sharing options...
Question
bonanova
Someone is willing to bet, at even odds, that if he throws six fair dice, exactly four distinct numbers will show.
For example 3 3 4 4 5 6 or 3 3 3 4 5 6.
Do you take the bet?
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