Question

In a​ lottery, the top cash prize was ​$657 ​million, going to three lucky winners. Players pick five different numbers from 1 to 53 and one number from 1 to 43.

A player wins a minimum award of $200 by correctly matching four numbers drawn from the white balls​ (1 through 53​) and matching the number on the gold ball​ (1 through 43​). What is the probability of winning the minimum​ award?

Answer 1

1 chance in 123,396,455

Explanation:

Number of permutations of 5 out of the 53 = 53*52*51*50*49 = 344362200

Number of permutations of 4 out of these 5 correct = 120

So number permuations for first 53 = 344362200/ 120 = 2869685

So for minimum prize there are 2869685 * 43 = 123396455 perms.