Wednesday, April 11, 2007

Permutations and Combinations April 11th

Hey, today we started off with Mental Math, which was really hard.

Also Mr.Max before I get started, because your such a vocabulary expert, take a stab at his question,

Is "sidewards" a word?....(don't try to look it up until you think you know the answer.)
Anyways, We then went over perms and coms. We learned and reviewed the formula for permutations that nPr=n!/(n-r)! and the formula for combinations it nCr=n!/(n-r)!*r!

Lets use one of the formulas in a question and see how it works...( we did this one in class )

Ok, you have 3 & 4 digit codes with 4 digits to choose from. (1,2,3,4)

Since you're trying to find out possible codes, it matters what order the numbers are in.

And since it matters what order the numbers are in, it is therefore a permutation. The formula for permutations is nPr=n!/(n-r)! where (n) is the total number of objects to be ordered or considered and (r) is how many objects at a time are ordered. ( If you have any other questions about factorials I put up a post under factorials that you can read, it might be of some help, Mr.Max also said that these formulas would be a good thing to put on a formula sheet.)

Anyways, so this works out to 4P3=4!/1!,

4! is the same as 4*3*2*1=24,

1! is the same as 1=1

therefore 4P3= 24/1

there are 24 ways to get 3 digit codes using the digits 1,2,3, and 4.

Then you had to figure out how many 4 digit codes you could have with the numbers 1,2,3 and 4. You still use the same formula.

Except this time, it works out to:


4! is the same as 24

0! is by definition equal to 1

this leave us with 4P4= 24/1 which is 24

This means that there are 24 ways to get a 3 digit code and 24 ways to get a 4 digit code.

A different way of getting the same answer is with your calculator. From your home screen you hit (n) (whatever the case may be) then MATH, over to PRB, then down to nPr or nCr, (what ever the case may be), and then ENTER, and then put in (r) (whatever the case may be)

Mr.Max said that you don't need to use these formulas if you don't want to, but you should understand then.

Also Mr.Max will be gone Tuesday, Wednesday, Thursday, and Friday, of next next week, ( I think that would be the 24th, 25th, 26th, and 27th, and he has the joy of going to talk to a bunch of teachers or something. He didn't look to enthusiastic about that. We will have a sub and probably just work on Accelerated Math, and other assigned questions.

Practice questions due for tomorrow are from the handout, #5, #11, and #14

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