# Thread: Permutations and Combinations Help!

1. ## Permutations and Combinations Help!

Hello, what are some ways/tips that i can use to help me distinguish between permutation and combination word problems?

2. Originally Posted by TheCB4
Help me distinguish between permutation and combination word problems?
If it involves order it is a permutation.
If only content matters then it is a combination.

How many ways can you make a four-letter string using the letters in $\displaystyle S~O~U~T~H~E~R~N$?
That is a permutation.

How many ways can you select four letters from $\displaystyle S~O~U~T~H~E~R~N$?
That is a combination.

3. Hello, TheCB4!

What are some ways/tips that i can use to help me distinguish
between permutation and combination word problems?
In a permutation, the order of the objects is important.

Suppose there are 10 books on the table
. . and you may select 4 of them.

If you choose the 4 books and place them in a row on a shelf,
. . it is a permutation.

There are: .$\displaystyle _{10}P_4 \:=\:\frac{10!}{6!} \:=\:10\cdot9\cdot8\cdot7 \:=\:5040$ possible arrangments.

If you choose the 4 books and toss them into a shopping bag,
. . it is a combination.

There are: .$\displaystyle _{10}C_4 \:=\:\frac{10!}{4!\,6!} \:=\:210$ possible selections.