Question

Mega Millions is a national lottery that is played as follows: You pick five different numbers from 1 to 70 then one number from 1 to 25. The Mega Millions web site lists odds ("chances") of winning, which in each case is listed as "1 in N" for some number N. In each case, these are essentially the fractions number of winning possibilities . number of possible lottery tickets (a) Verify that the chances given on the page for winning the jackpot ("1 in 302,575,350") is correct using this rationale. This basically means: verify that the number of possible lottery tickets is 302, 575, 350.

Answer 1

The chances given on the page for winning the jackpot ("1 in 302,575,350") is correct.

Explanation:

We just have to verify that the number of possible lottery tickets is 302, 575, 350.

We have six numbers

N1 - N2 - N3 - N4 - N5 - N6

The first five numbers are a combination of 5 from 70. This is a combination because for example, 1,2,3,4,5 is the same as 5,4,3,2,1.

The total number of combination of x from n is given by the following formula:

`C_(n,x) = (n!)/(x!(n-x)!)`

The sixth number can be any of the 25 values.

The total number of combinations is:

`T = C_(70,5)*25 = 302,575,350`

This means that the chances given on the page for winning the jackpot ("1 in 302,575,350") is correct.