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How many paths are there from \(C\) to \(B\) , if every step must be up or to the right?

Guest Jun 16, 2018

#1**+2 **

The path from C to B must have two steps up and four steps right.

The possibilities are:

up, up, right, right, right, right

up, right, up, right, right, right

up, right, right, up, right, right

up, right, right, right, up, right

up, right, right, right, right, up

right, up, up, right, right, right

right, up, right, up, right, right

right, up, right, right, up, right

right, up, right, right, right, up

right, right, up, up, right, right

right, right, up, right, up, right

right, right, up, right, right, up

right, right, right, up, up, right

right, right, right, up, right, up

right, right, right, right, up, up

That is a total of 15 possibilities.

I remember a similar question to this: https://web2.0calc.com/questions/help-1_2

Checking it using the formula heureka showed...

\(\frac{(2+4)!}{2!4!}=\frac{6!}{2!4!}=\frac{6\cdot5\cdot4\cdot3\cdot2\cdot1}{2\cdot1\cdot4\cdot3\cdot2\cdot1}=\frac{6\cdot5}{2\cdot1}=\frac{30}{2}=15\)

Also gives the answer 15

hectictar Jun 17, 2018