Who’s the bigger sucker, a lottery player or a keno player?
Also while in Vegas, Greg and I were arguing over the relarive merits (or lack thereof) of playing keno and the lottery. There is an excellent website by HREF="http://mathforum.org/dr.math/faq/">Dr. Math that has all kinds of goodies on math in everyday life situations. The one dealing with HREF="http://mathforum.org/dr.math/faq/faq.comb.perm.html">combinations and permutations is partiuclarly relevant for this question. Both keno and regular
lotteries are examples of combinations, where the order does not matter (Powerball is a mix of combinations and permutations, since the powerball order does
matter). The formula is C(n,k)=n!/(k!(n-k)!), where n is the number of objects to choose from, and k is number chosen. For a lottery where you pick 6 numbers
out of 54, there are 54!/(6!(54-6)!) possible combinations, which is 54*53*53*51*50*49/(6*5*4*3*2), or a 1 in 25,827,165 chance of getting all six. In Keno,
picking 20 out of 80, there are 80!/(20!(80-20)!) combinations, which is 80*79*…*62*61/(20*19*…*2*1), or 3.535316142212174e+18. That’s more than 3.5
quintillion to 1! That’s how they make the buffets so cheap!