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# How many paths are there from to , if every step must be up or to the right?

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

Jun 16, 2018

#1
+8170
+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...

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

Jun 17, 2018
#2
+101768
+2

That is interesting Hectictar.

I know it is Heureka's formula but I don't remember seeing it before.

Melody  Jun 17, 2018
#3
+1

CPhill used this formula three years ago on this post.

https://web2.0calc.com/questions/mack-the-bug-starts-at-0-0-at-noon-and-each-minute-moves-one-unit-right-or-one-unit-up-he-is-trying-to-get-to-the-point-5-7-howeve

Guest Jun 17, 2018