How many paths are there from \(C\) to \(B\) , if every step must be up or to the right?
+9466 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 
