Question

6 bananas are to be selected from a group of 8. In how many ways can this be done?

Answer 1

There are `28` ways of selecting `6` out of `8` bananas

Explanation:

The easiest way to calculate this is to note that `2` bananas are to be not selected.

There are `8` ways to choose the first non-selected banana
and for each of these ways there are `7` ways of choosing the second non-selected banana.

This gives `8xx7=56` ways of choosing a first and second banana to not be selected...
but since this double counts the choice since choosing banana P first and banana Q second has the same effect as choosing banana Q first and banana P second.

So the actual number of ways of doing this is `(8xx7)/2=28`

In factorial notation this could be written as `(8!)/(2!*6!)`