Question

Question #0dedf

Answer 1

`70`

Explanation:

Assuming the `8` objects are distinct, then this is equivalent to the number of ways of choosing `4` objects from the group of `8`, as if that is the first group, then the remaining `4` is decided as the second group.

The number of ways of choosing `k` objects from a set of `n` objects can be calculated as

`((n),(k)) = (n!)/(k!(n-k)!)`

(read as `n` choose `k`)

Applying this to the given question, we have the number of ways of choosing a set of `4` objects from a set of `8` as

`((8),(4)) = (8!)/(4!(8-4)!)`

`=(8*7*6*...*3*2*1)/((4*3*2*1)(4*3*2*1)`

`=(8*7*6*5)/(4*3*2*1)`

`=70`