Combination or permutation?

if the lottery demands

that the numbers be predicted in the order in which they are drawn,

then it is permutations

if the lottery demands

that the numbers be predicted regardless of order,

then it is combinations

Lottery Permutations

Let her choose the ribbons one by one. For the first one, she has 6 options. For the second one, there are 5 options left. So there are 30 different ways of selecting an ordered pair of ribbons. However, Cathy doesn't care about the order. Taking first a blue and then a white ribbon is the same as taking a white ribbon first and then a blue one. This means we counted double the number of possibilities. So the actual number is 5*6 / 2 = 15. This is, in effect, a combination: 2C6. The reasoning behind the formula for combinations is as follows: You can put all six ribbons in 6! different orderings. Of the six sorted ribbons you would then select the first two. As you don't care about the order of these two, you can divide the number by the number of ways of ordering those two: 2!. The same goes for the four ribbons Cathy did not select: these can be in 4! different orderings. So the total number of possible combinations is 6! / (2! 4!)