C(n,r) = [n!/((n-r)!*r!)] . n is the number of possibilities and it is 52 in question and r is the number of things to be taken at a time which is 6 . if we substitiue . C(n,r) = [52!/((52-6)!*6!)= 52!/((46)!*6!)] . 52! = 52*51*49*48*47*46*45*44*43*42*..... and 46! = 46*45*44*43*42*.... .
you divide 52! by 46! the result after canceling all the common terms is just 52*51*50*49*48*47. The question is reduced to . C(n,r) = (52*51*50*49*48*47)/6! . and 6! = 6*5*4*3*2*1 . If you want you can divide the numbers from 6! into the numbers in the numerator to simplify things a little or you can just take your calculator and multiply out the numerator and then divide that answer by 720 which is what 6! equals. . If you just multiply out the numerator your calculator should tell you that the answer is 1.46581344*10^10 and when you divide that by 720 you get 20,358,520. This means that for every 20,358,520 lottery tickets sold there is likely to be 1 winner among them. Pretty slim odds of your ticket being that one. .
If you have a cheap scientific calculator you might examine it carefully to see if it has a key function labeled nCr. If you do it will calculate this combination automatically. . Just enter 52, then press the nCr function, then enter 2, and press the equal sign.
