Question

permutations: point b is 4 blocks east and 5 blocks north of point a. point c is 7 blocks north and 4 blocks east of point b. how many paths are there from a-c if u only travel north and east?

Answer 1

Do you have to pass through b?

Answer 2

nope

Answer 3

There are 8 east and 12 north in total.

Answer 4

ok

Answer 5

In an mxn grid, the number of paths is given by \[(m+n)! \div n! \div m!\]
At least, it worked on the small grids I just thought about.

Answer 6

@agent0smith do you understand this ?

Answer 7

Factorials are given by \[ x!\]
x factorial is x * (x-1) * (x-2) * ... * (2) * (1)

Answer 8

So this would be 20! divided by 12! and 8! It makes sense when you consider that there are 20 choices to be made which could be made in any order and will get you to the same endpoint. It doesn't matter whether a certain move east or north is the 2nd or the 7th, though, so you have to divide by 8! (for east) and 12! (for north)

Answer 9

divided by 12!x8!?

Answer 10

or 12!+8!É

Answer 11

12!*8!. 20!/(8!*12!) can be rephrased as 20*19*18*17*16*15*14*13/(8*7*6*5*4*3*2*1) (everything 12 and below cancels with 12!) I highly recommend cancelling before multiplying.

Answer 12

So with cancellation we get:
\[10*19*3*17*13=125970\]

Answer 13

imo it's just simpler to evaluate as is. Most calculators have a factorial button, and you aren't learning a whole lot by cancelling off factors, but you are leaving the door open to simple arithmetic errors which could be avoided.

20!/(8!*12!) =
https://www.google.com/search?q=20!%2F(8!*12!)&aq=f&oq=20!%2F(8!*12!)&aqs=chrome.0.57&sourceid=chrome&ie=UTF-8

Answer 14

It's good to know about cancelling so that if you want to impress people you can do it in your head more easily. I know almost any exam would allow calculators at this point, but if you don't carry one with you it's still a nice trick to know. @agent0smith Simpler, in terms of the human input, yes. More efficient (in terms of computation time), yes (computers are faster than humans, so they cancel these factors faster than you or I ever could). Not quite as fun, though!

Answer 15

haha, but that was one thing i forgot to mention - time.

While you're impressing people doing it in your head, someone with a calculator is saying "I already have the answer" :P

And if you make a mistake doing it in in your head, such as accidentally dropping a number, then you've wasted more time AND have the wrong answer.

Answer 16

That's assuming that someone else has all of these:
A calculator
Knowledge of what the heck they're doing
Interest enough to do it.

Also, if none of the above are true very few people around you would be able to catch an error.

Answer 17

haha, so you can be wrong, but no one will know... reminds me of this

"If a man is alone in a forest and there are no women around to hear him speak, is he still wrong?"