Kristan Nov. 01

Permutations and Combinations

Or, “Perms and Coms” for those of us who love simple terms.

Consider the letters, A, B, C, D, E

How many different “words” can we make using the FCP to solve this problem?

First thing you have to know is, ORDER MATTERS!!!!!!! In solving a PERMUTATION.

“ABCDE” is different from “ABCED”

and how do you find out how many “words” this is? Well, you go,

5 x 4 x 3 x 2 x 1

= 5!

=120 ways

But say we used the whole alphabet, what then?

26 x 25 x 24 x 23 x 22

=7,893,600 ways to permute 26 letters.

OR

26 letters permuted 5 at a time.

Hmm…. Or you could go…

(26 x 25 x 24 x 23 x 22) x 21!

21!

26!

21!

and voila! It = 7,893,600

or

nPr = “n things permuted r at a time”

= 26 letters permuted 5 @ a time.

The Calculator button presses to do this all the easy way are,

26 > Math button > PRB> nPr > 5 and Enter

n = total # of elements to draw from

r = How many elements at a time

Here is an example of permutation…

Remember, ORDER MATTERS!!!!

Say you have a security code with 4 digits, and there are no repeats.

You could go the long way and type in,

10 x 9 x 8 x 7

= 5040 ways

OR…

nPr……10 P 4 = 5040 ways.

Now onto COMBINATIONS

Examples in heart’s and diamonds’s.

How many different poker hands (5 card hand)

In a combination ORDER DOESN’T MATTER!!!!!

26 x 25 x 24 x 23 x 22

=7,893,600 NO!!!! But… THIS ISN’T THE RIGHT ANSWER…

You have to “Divide out the doubles.”

You should go,

(26 x 25 x 24 x 23 x 22)

5 x 4 x 3 x 2 x 1

= 65,780

nCr = n!

(n-r)!-r! <<>

basically, 26!

(26-5)!-5!

= 26!

21! – 5!

= 65780

26 C 5

26 cards Chosen 5 @ a time where order DOESN’T matter!
26 – math – nCr- 5

= 65780

Combinations end up with a smaller result number.

Permutations end up with much larger result numbers.

The scriber for Wednesday is Melissa07

~Kristan~