1) consider the number of grid paths from the orgin in a coordinate graph to each of the following points:

Question

a) (4,7) b) (3,7) c) (4,6)

2) simplify: (n-r)! / (n-r+1)!

3) solve (n+2)!/ (n-1)! = 210

Answer 1

A),B),C)
It's like finding the number of ways to arrange 4 1's and 7-0's.
The number of ways is given by (m+n)!/(m!n!)
Experiment first with a grid of 2x2, and then a 2x3.

2.
(n-r)!/(n-r+1)!
=(1.2.3...n-r)/(1.2.3...(n-r).(n-r+1))
=1/(n-r+1)

3.
similarly,
(n+2)!/(n-1)! = 210
(1.2.3...(n+2))/(1.2.3...(n-1)) = 210
n.(n+1).(n+2) = 210
Start with cube root of 210 = 5.9...
so try 5.6.7=210 OK.
So n=5,n+1=6,n+2=7

Answer 2

thank even though im not sure if u woule see this

Answer 3

You're welcome!