Question

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

Answer 1

Answer:

$\frac{1}{4845}$ probability that you and your 3 friends will be selected.

Step-by-step 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.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Desired outcomes:

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

$D = C_{4,4} = \frac{4!}{4!0!} = 1$

Total outcomes:

20 people from a set of 20. So

$T = C_{20,4} = \frac{20!}{4!16!} = 4845$

Probability:

$p = \frac{D}{T} = \frac{1}{4845}$

$\frac{1}{4845}$ probability that you and your 3 friends will be selected.