Question

In the Minnesota Northstar Cash Drawing, you pick five different numbers between 1 and 35. What is the probability of picking the winning combination (order does not matter)

Answer 1

`(1)/(324632)` probability of picking the winning combination

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Since the order is not important, the combinations formula is used to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

Desired outcomes:

The correct five numbers from a set of 5. So

`D = C_(5,5) = (5!)/(5!0!) = 1`

Total outcomes:

Five numbers from a set of 35. So

`T = C_(35,5) = (35!)/(5!30!) = 324632`

Probability:

`p = (D)/(T) = (1)/(324632)`

`(1)/(324632)` probability of picking the winning combination