On the xy-plane, the origin is labeled with an M. The points (1,0), (-1,0), (0,1), and (0,-1) are labeled with A's. The points (2,0), (1,1), (0,2), (-1, 1), (-2, 0), (-1, -1), (0, -2), and (1, -1) are labeled with T's. The points (3,0), (2,1), (1,2), (0, 3), (-1, 2), (-2, 1), (-3, 0), (-2,-1), (-1,-2), (0, -3), (1, -2), and (2, -1) are labeled with H's. If you are only allowed to move up, down, left, and right, starting from the origin, how many distinct paths can be followed to spell the word MATH?

I NEED THIS AS MUCH AS I NEED WATER!!!!!!!!!! (which isn't much. I drink half a cup a day)

ProffesorNobody Apr 24, 2019

#1**+1 **

I wanna cuss but I can't haha but I need to vent everyday.

PLEASE PLEASE PLEASE PLEASE PLEASE PLEASE FORMAT PLEASE PLEASE

I'm like really pissed idek why this infuriates me. I have to give you props for effort in at least putting it in latex instead of others who just paste it in.

1) Spaces are removed in LaTeX

2) LaTeX in this forum is for EQUATIONS only

3) Noone will solve your question if you make it completly illegible, is shows little effort

4) This problem is totally OK with just text, just go to Notepad and CTRL+H and find and delete the H.

5) I like your username

So yeah. Reformat and me or someone will try to solve your question.

Bxtterman Apr 24, 2019

#6**+1 **

You can solve this problem easily by plotting it in on a coordinate plane and probability.

**NOTE BEFORE WE START. I MAKE MISTAKES AND I HAVE IN THE PAST PLEASE CHECK THIS ANSWER!**

Thank you for reformatting.

I just graphed this. it's a diamond with equal side lengths.

We first see that there are 4 ways to get to the first letter, **A**

We add the first part to our equation: \(1\cdot4\)

From A, we can get to the next letter, **T**

We can get to there **2 **ways from every A.

Our equation is now: \(1\cdot4\cdot3\)

Finally, we can get to the letter **H. **

For 4 of the 8 letter T's there are 2 H's.

Our equation is now \(1\cdot4\cdot3\cdot2=24\)

Next, we count the other 4. We have 3 H's for every T.

\(1\cdot4\cdot3\cdot3=36\)

We can add both cases:

\(24+36=\boxed{60}\)

Thank you man, I probabaly got this one wrong it's 1 AM and I'm answering math problems smh.

Bxtterman Apr 24, 2019