Combinatorics/Orders Problem? NEED HELP PLEASE PLEASE PLEASE

Several children were playing in the ugly tree when suddenly they all fell.

Roger hit branches A, B, and C in that order on the way down.

Sue hit branches D, E, and F in that order on the way down.

Gillian hit branches G, A, and C in that order on the way down.

Marcellus hit branches B, D, and H in that order on the way down.

Juan-Phillipe hit branches I, C, and E in that order on the way down.

Mikey hit every branch A through I on the way down. Given only this information, in

how many different orders could he have hit these 9 branches on the way down?

Re: Combinatorics/Orders Problem? NEED HELP PLEASE PLEASE PLEASE

$\displaystyle gabicdefh$

$\displaystyle gaibcdefh$

$\displaystyle giabcdefh$

$\displaystyle igabcdefh$

Re: Combinatorics/Orders Problem? NEED HELP PLEASE PLEASE PLEASE

Thanks. So those are the only four orders?

Re: Combinatorics/Orders Problem? NEED HELP PLEASE PLEASE PLEASE

Re: Combinatorics/Orders Problem? NEED HELP PLEASE PLEASE PLEASE

Thanks. Is there a reason that you put all the gs first? I mean why could it not just be abcdefgh? Once again thanks a lot

Re: Combinatorics/Orders Problem? NEED HELP PLEASE PLEASE PLEASE

Re: Combinatorics/Orders Problem? NEED HELP PLEASE PLEASE PLEASE

This got me curious. Is there a truly mathematical way of developing an answer? Just a curiosity. I was wondering if somehow you could list the branches in order, and resolve an answer without manually counting all of the possibilities.

Re: Combinatorics/Orders Problem? NEED HELP PLEASE PLEASE PLEASE

Yes there is a way to develop the answer mathematically. Word the question like this.

Mikey has 9 cards in front of him, in how many different ways can he pick up the 9 cards?

Well....

1,2,3,4,5,6,7,8,9

1,2,3,4,5,6,7,9,8

1,2,3,4,5,6,8,9,7

ect. You should have been taught about factorials. The factorial of a number is calculated as.

$\displaystyle 9! = 1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9$

You'll most certainly need a calculator because factorials grow at an insane rate for each digit you add. Go ahead and type that into your calculator.

P.S The branch example is a terribly worded question because one can assume you can't hit branch I before hitting branch A. So if one falls one can only hit the branches in letter order progressing alphabetically.

Re: Combinatorics/Orders Problem? NEED HELP PLEASE PLEASE PLEASE

Quote:

Originally Posted by

**MaxJasper** $\displaystyle gabicdefh$

$\displaystyle gaibcdefh$

$\displaystyle giabcdefh$

$\displaystyle igabcdefh$

It seems to me there are some missing possibilities.

How about

I G A B D H C E F

for example?

Re: Combinatorics/Orders Problem? NEED HELP PLEASE PLEASE PLEASE

Would a simple nCr function work to some extent, to help to figure out the number of combinations maybe ?

Re: Combinatorics/Orders Problem? NEED HELP PLEASE PLEASE PLEASE

Could someone please figure this out and show me how they got the answer please? My test is on Sunday, I have to go into school to take it. Thanks so much.