What is the probability, as a fraction, of winning the jackpot?

Question

In the Mega Millions lottery game, you choose 5 different numbers between 1 and 70, and one additional number between 1 and 25. If you get all 6 numbers correct, you win the jackpot.

Answer 1

By choosing 5 different numbers from 1 to 70, the number of combinations possible is:

₇₀C₅ = 70!/(5!(70-5)!) = (70*69*68*67*66)/(5*4*3*2*1) = 12,103,014

Additionally, with choosing a 6th number from 1 to 25, the number of combinations possible is:

₂₅C₁ = 25!/(1!(25-1)!) = 25

This means that the probability of selecting all 6 numbers correctly and winning the jackpot is 1/12,103,014 * 1/25 = 1/302,575,350

Coincidentally, this is the same probability for matching all 5 numbers in the Mega Millions plus the Mega Ball!

Hope this helped!