2 In the NYS lottery game called Pick6 Lotto you select six

2. In the NYS lottery game called Pick-6 Lotto; you select six numbers of your choice from a set of numbers ranging from 1 to 53. We can apply the Combination Rule to determine the total number of combinations of 6 numbers selected from 53, how many combinations are there?

Solution

number of combinations when selecting 6 six numbers of your choice from a set of 1 to 53, total of 53 numbers be = 53 C 6 = 53! / (53-6)!*6! = 53!/47! * 6! = (53*52*51*50*49*48*47!) / 47! * 6! = (53*52*51*50*49*48)/ 6! = 22957480 set of combinations are possible