Permutations and Combinations Help!

• Nov 25th 2009, 12:26 PM
TheCB4
Permutations and Combinations Help!
Hello, what are some ways/tips that i can use to help me distinguish between permutation and combination word problems?
• Nov 25th 2009, 01:29 PM
Plato
Quote:

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.
• Nov 25th 2009, 06:38 PM
Soroban
Hello, TheCB4!

Quote:

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.