Question

There are 6 balls, all uniquely coloured, in a bag. We're randomly drawing 2. How many ways can we draw first Blue, then White? How many ways can we draw the colour combination of Blue and White?

Answer 1

`P_(6,2)=30; C_(6,2)=15`

Explanation:

We have 6 marbles and are pulling out 2.

The first question asks about colour sequences (and so Blue, White is different than White, Blue) and so is a permutation. The general formula is:

`P_(n,k)=(n!)/((n-k)!); n="population", k="picks"`

`P_(6,2)=(6!)/((6-2)!)=(6!)/(4!)=(6xx5xx4!)/(4!)=30`

The second part of the question asks about colour combinations, and so Blue, White is the same as White, Blue. That is a combination and the general formula is:

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

`C_(6,2)=(6!)/((2!)(6-2)!)=(6!)/((2!)(4!))=(6xx5xx4!)/(2xx4!)=15`