Question

Congress is finally running our country into the abyss of out of control debt and deficits. As a last resort to generate income, the presidential lottery has been created. In this lottery, a total of 7 numbers will be chosen. The player picks 6 numbers between 1 and 57 with no duplicates. The 7th number will be selected between 1 and 19. a) What is the probability of matching all 7 numbers and winning the presidential lottery? b) What is the probability of winning if you pick your numbers in the same order that the winning numbers are selected?

Answer 1

a)

Number of ways to picks 6 numbers between 1 and 57 = ⁵⁷C₆ = 57! / [(57-6)! * 6!]

= (57 * 56 * 55 * 54 * 53 * 52) / (6 * 5 * 4 * 3 * 2 * 1) = 36288252

Number of ways to picks 1 number between 1 and 19 = ¹⁹C₁ = 19

Total number of ways to pick 6 numbers between 1 and 57 with no duplicates and 7th number from 19 numbers = 36288252 * 19 = 689476788

Probability of matching all 7 numbers and winning the presidential lottery = 1 / 689476788

b)

Number of ways to picks 6 numbers between 1 and 57 in the same order = ⁵⁷P₆ = 57! / (57-6)!

= (57 * 56 * 55 * 54 * 53 * 52) = 26127541440

Number of ways to picks 1 number between 1 and 19 = ¹⁹C₁ = 19

Total number of ways to pick 6 numbers between 1 and 57 with no duplicates and 7th number from 19 numbers in the same order = 26127541440 * 19 = 496423287360

Probability of winning if you pick your numbers in the same order that the winning numbers are selected = 1 / 496423287360