Question

Discrete Mathematics paths help. Picture provided.

Answer 1

@dan815

Answer 2

game of choosing

Answer 3

a certain number of east and a certain number o north

Answer 4

are required to travel your path so

Answer 5

its how many ways you can choose the c1 Norths and c2 Easts

Answer 6

(n-1) norths and (n-1) easts ?

Answer 7

or i should say i Easts and j norths

Answer 8

yeah from 1,1 so it should be picking n-2 Norhs and n-2 Easts right?

Answer 9

choosing*

Answer 10

I'm a bit confused on how that would look equation wise. Or can it be put into an equation?

Answer 11

oh sry wait i was just answering that thought in their question where they want to go from
1,1 to (n-1,n-1)

Answer 12

Are you talking about part a?

Answer 13

is a asking if we are i,j... how many ways are there to reach n-1,n-1?

Answer 14

that would be
(n-1-i) east and (n-1-j) north to choose from

Answer 15

which is
((n-1-i)+(n-1-j) )+choose (n-1-i)

Answer 16

((n-1-i)+(n-1-j) )choose (n-1-i)

Answer 17

for n=5

Answer 18

so u have 4 North an 4 east in n=5 so
8C4=70

Answer 19

\[\large \binom{2(n-1)}{n-1}\]

Answer 20

would that work dan

Answer 21

yeah for B right

Answer 22

for d) i mean

Answer 23

in general.. for a square grid..

Answer 24

yep

Answer 25

yes...

Answer 26

for part a, im still trying to understand how u got below :
((n-1-i)+(n-1-j) )choose (n-1-i)