Tuesday, February 27, 2007

9.4 Probabilities of Various Permutations

Hey everybody!

Here is some info about PERMUTATIONS!

permutations are a way to count the number of outcomes when the ORDER is important.

A really simple way of doing these types of problems is with factorials, ! .
For instance: 9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880.
To do this on the calculator, either multiply the entire system out or go to MATH, PRB, 4: !

Some problems that use this are...

If you have 7 people trying to share 3 spots, you have to divided 7! by 4!. It is 4! because you subtract the number of spaces from the total number of people. When you do this, the 4 x 3 x 2 x 1 cancels out, leaving 7 x 6 x 5 = 210.

Repeated Elements: If there is a word or something with repeating figures: take the factorial of the total number of figures/ factorial of repeating figures. NEEMATOAD (frog-like swamp monster): 9 total letters, 2 repeated A's and 2 repeated E's, so 9!/(2! x 2!) = 90,720 total distinct combinations.

Restrictions: If you have 10 people who need to fill 10 spots but 3 are restricted to specific persons, the number of possibilites is 7! x 1 x 1 x 1 = 5040. The three 1's show that there are no additional outcome because of the 3 restricted spots.

Practice Problem!

A. On the Winnie the Pooh ride at Disneyland each cart has enough room for 4 people. Danny and Michelle are dating, and must therefore sit together, but there are 6 people with them who can sit any where. Within the
two carts how many possible seating arrangements are there?

B. While waiting in line, Dieter, Danny's friend, was wondering how many distinct combinations the letters in the ride name (including "the") could be made into. Find this number.

Solutions!

A. To find this number, take the number total, 8!, and divide by 4, the number of possibilities for where they can sit. The answer is 10,080.

B. First you need to count the total number of letters, 13. Then count the number of repeats. There are two pairs. The number is 13!/(2! x 2!) = 1,556,755,200.

For more help, check out

http://mathforum.org/dr.math/faq/faq.comb.perm.html

I hope this was helpful. And this has been fun with Permutations!

here is a video with stop motion, drums, and piano!!! IT'S AWESOME
http://youtube.com/watch?v=hVG_esC-rgA
it actually sounds good too...

MARICLARE you're next!!








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