Question

What is a combination?

Answer 1

See below:

Explanation:

A combination is a grouping of distinct objects without regard to the order in which the grouping is made.

As an example, a poker hand is a combination - we don't care in what order we're dealt the cards, only that we're holding a Royal Flush (or a pair of 3s).

The formula for finding a combination is:

`C_(n,k)=((n),(k))=(n!)/((k!)(n-k)!)` with `n="population", k="picks"`

As a for instance, the number of possible 5-card poker hands is:

`C_(52,5)=(52!)/((5)!(52-5)!)=(52!)/((5!)(47!))`

Let's evaluate it!

`(52xx51xxcancelcolor(orange)(50)^10xx49xxcancelcolor(red)48^2xxcancelcolor(brown)(47!))/(cancelcolor(orange)5xxcancelcolor(red)(4xx3xx2)xxcancelcolor(brown)(47!))=52xx51xx10xx49xx2=2,598,960`