3) In the word REARRANGE we have 9 letters.
For these letters to be distinct, we must think of each letter like a gumball in a gumball machine. Every time I use one, there of less to be used.
We also need casework for each length of word:
CASE 1: 1 letter words
9 one letter words.
CASE 2: 2 letter words
\(9\cdot8=72\) two letter words
CASE 3: 3 letter words.
CASE 4: 4 letter words
CASE 5: 5 letter words
CASE 6: 6 letter words
CASE 7: 7 letter words (almost done!)
CASE 8: 8 letter words
CASE 9: (DONE!)
Now we add all the cases together for the total number of arrangments:
You can subsitute the decending numbers with a factorial
Just some rules for future reference, hope you enjoy and use them.
As always if you have any questions just ask.
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.
We can add both cases:
Thank you man, I probabaly got this one wrong it's 1 AM and I'm answering math problems smh.
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.