Answer:
4,690,625,500 different samples are possible.
Step-by-step 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.
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, we have that:
Number of combinations of 6 from 125. So
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
[tex]C_{125,6} = \frac{125!}{6!(119)!} = 4,690,625,500[/tex]
4,690,625,500 different samples are possible.
