How would you calculate Super Lottory odds?

Question

Based on my calculation, the number of possible combinations is:
47 * 46 * 45 * 44 * 43 * 27 = 4 969 962 360
just about 1 in 5 Billion

Yet, http://www.calottery.com/Games/SuperLottoPlus/HowtoPlay/ lists the odds as 1 in 41,416,353

How are they calculating the odds?

Answer 1

The number of combinations of n items chosen from m items is: (m!)/(n!*(m-n)!).

What you forgot to do is divide your number by (5!), or 120. When you do this, you'll get the same number as the SuperLottery website.

If you don't divide by n!, you get the number of permutations. The difference is that in permutations, the order of the numbers matters. In combinations (like the lottery), the order doesn't matter.