Question

You tell your 3 friends that you are going to a magic show. It turns out, in an amazing coincidence, they each

have tickets to the same magic show. The dissapointing part is that all 4 of you are sitting in different places at
the event. During the show, the magician asks for 4 brave volunteers. If you and all of your friends raise your
hands as well as 16 other audience members for a grand total of 20 volunteers.
What is the probability that you and your 3 friends will be selected. Write your answer as a simplified
fraction.

Answer 1

`(1)/(4845)` probability that you and your 3 friends will be selected.

Explanation:

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

In this question, the order in which the volunteers are chosen is not important, which means that 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:

You and the 3 friends(4 people), from a set of 4. So

`D = C_(4,4) = (4!)/(4!0!) = 1`

Total outcomes:

20 people from a set of 20. So

`T = C_(20,4) = (20!)/(4!16!) = 4845`

Probability:

`p = (D)/(T) = (1)/(4845)`

`(1)/(4845)` probability that you and your 3 friends will be selected.