Question

A coin collector has a box that contains 125 unique coins. a. If you take a sample of six coins, how many different samples are possible

Answer 1

4,690,625,500 different samples are possible.

Explanation:

The order of coins in the sample is not important. For example, if our box is:

A-B-C-D-E-F

It is the same as

F-A-B-C-D-E

So we use the combinations formula to find how many different samples are possible.

`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)!)`

In this problem, we have that:

Number of combinations of 6 from 125. So

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

`C_(125,6) = (125!)/(6!(119)!) = 4,690,625,500`

4,690,625,500 different samples are possible.