Question

HELP ME! I WILL MEDAL AND FAN!!!

Answer 1

Your ultimate goal is to determine how many paths there are from S to *.
a. You can either go straight down one box
b. Or, you can go to the right one box
c. Down and right is not the same as right and down, that's 2 different paths
d. You can't go left, up or diagonally

Answer 2

No matter what, you need to go down 4 times, and right 5 times. It's just a matter of ordering them.

Answer 3

Also, this problem is too difficult to be assigned in elementary, if you ask me

Answer 4

its not

Answer 5

Anyway, since we're just assigning ordering to the downs and rights, I say assign the downs and let the rights fall into place. There are \(4+5\) spots to place a down, and there are \(4\) downs. We will use the choose operation.

Answer 6

its for 8th grade mathematics

Answer 7

Which would mean: \[
5+4\choose 4
\]

Answer 8

\[Did you mean \frac{ 5+4 }{ 4 } ?\]

Answer 9

You are in 8th grade? I commend you.

Answer 10

No, it's not a fraction... It seems you don't know combinatorics... you'll have to use a harder way? hmmmm

Answer 11

lol im actually in 7th but im boing 8th for math since inm in the gited program

Answer 12

What have they taught you?

Answer 13

pascal's triangle???

Answer 14

Yes! We'll use pascals triangle

Answer 15

So basically \[
5+4 \choose 4
\]Means that we will create \(5+4\) rows, and then we will pick the \(4\) column of that row.

Answer 16

Can you build this triangle?

Answer 17

Okay hmmmm

Answer 18

Okay, so I stand corrected...
We need to go the tenth row, and we need the 5th column

Answer 19

Row 10 column 5 will be 126

Answer 20

@FireWolfSpirit

Do you need a better explanation?

Answer 21

One way to think about this is that we have \(d\) and \(r\) representing down and right respectively.

Answer 22

We need to move a total of \(9\) spaces.

Answer 23

The number of ways we would move down or right will be \(d+r\)

Answer 24

The number of ways to do this \(9\) times is: \[
(d+r)^9
\]

Answer 25

This is the total number of ways we can move down or right.

Answer 26

However, we really only want to move down 4 times and right 5 times.
This is represented by \(d^4r^5\).

Answer 27

So we want the coefficient of the term \(d^4r^5\).

Answer 28

That is why we use pascal's triangle.

Answer 29

\[
\begin{array}{ccccccc}
&&&1 d^0r^0\\
&&1d^1r^0&&1d^0r^1\\
&1d^2r^0&&2d^1r^1&&1d^0r^2\\
1d^3r^0&&3d^2r^1&&3d^1r^2&&1d^0r^3\\
\end{array}
\]

Answer 30

So I am not going to get the medal or fan?

Answer 31

He/she appears offline.