Question

For the Decades of Dollars lottery game in Georgia, a player chooses 6 different numbers from 1 to 47, inclusive. To win the jackpot, all 6 numbers without regard to order should match the winning pick. What is the probability of winning the jackpot?

Answer 1

1/10,737,573

Explanation:

The number of possible outcome is

47 combination 6

nCr=n!/(n-r)!r!

Then,

47C6 = 47!/(47-6)!6!

47C6=47!/41!6!

47C6=47×46×45×44×43×42×41!/41!6×5×4×3×2×1

47C6=47×46×45×44×43×42×/720

47C6=10737573

This the sample space of groups 6 numbers.

So to win a jackpot, you need to pick one of the possible outcome

P(winning jackpot)= 1/10,737,573

Wow, this result shows that it is not easy to win a jackpot from lottery games, it is on rare occasions to have the combine 6 numbers.