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 Dr. Math that has all kinds of goodies on math in everyday life situations. The one dealing with 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!