Question

Choosing seven numbers that match seven randomly selected balls when the balls are numbered 1 through 32?

Answer 1

Total numbers = 32
We are to select 7 numbers at a time. Selecting 7 numbers from a group of 32 is a combination problem. It is similar to making combination of 32 objects taken 7 at a time.

So total possible combinations of 7 numbers can be calculated as 32C7.

32C7 = 3365856

Only 1 combination can match the randomly selected combination. 

So, the probability that he combination of 7 numbers will match the seven randomly selected balls = $\frac{1}{3365856}$