Probability and Combinations

Key Questions

• A permutations is an arrangement, so the order of its elements matters; on the other hand, a combination is a subset, so the order of its elements does not matter.

Example

All permutations of two elements from $\left\{a , b , c\right\}$ are:

$a b , b a , a c , c a , b c$, and $c b$

All combinations of two elements from $\left\{a , b , c\right\}$ are:

$\left\{a , b\right\} , \left\{a , c\right\}$, and $\left\{b , c\right\}$

I hope that this was helpful.

• I need more details to answer this question. This is a video my co-teacher and I made. Hope it helps, if not please give me some details and I will try to do better.
http://www.frontporchmath.com/topic/probability-using-tree-diagram-bagel-grab-bag/

• Combinations of items are basically subsets of the items, so the number of combinations is the number of subsets of items.

Let $C \left(n , r\right)$ denote the number of combinations of $n$ item chosen $r$ items at a time. Then, it can be found by

C(n,r)={P(n,r)}/{r!}={n cdot (n-1) cdot (n-2) cdot cdots cdot (n-r+1)}/{r!}={n!}/{(n-r)! r!}

Example

Find the number of ways to choose 3 cookies out of 6 distinct cookies.

C(6,3)={P(6,3)}/{3!}={6cdot5cdot4}/{3cdot2cdot1}=20

Hence, there are 20 ways to choose 3 cookies from 6 cookies.

I hope that this was helpful.