# The ant is moving through the coordinate system, Started at $(0,0)$ to $(4,4)$. What is the probability that the ant will find food at $(3,2)$?

The path to the $(3,2)$ is $3+2 \choose 3$ or $3+2 \choose 2$.

Total path is $4+4 \choose 4$

And the probability is : $\frac{3+2 \choose 3}{4+4 \choose 4}$ =

$\frac{5 \choose 3}{8 \choose 4}$ = $\frac{10}{70}$ = $0.14$

I am not sure if I solved this problem corectly.

• You're missing part of the problem statement: How does the ant move through the coordinate system? Does it always move by $+1$ in either the $x$ or $y$ directions? Sep 3 '15 at 16:53
• Steps are 1 the the right or 1 up. $(1,0)$ or $(0,1)$
– user258209
Sep 3 '15 at 16:59
• @SandroBrljafa: Is "the ant will find food at $(3,2)$" the same as "the ant will pass through $(3,2)$" in the question? (Is food always there?) Sep 3 '15 at 17:30
• @mathlove the food is always there
– user258209
Sep 3 '15 at 17:31

It is not correct. Note that there are $\binom{3}{1}$ ways from $(3,2)$ to $(4,4)$.
• $5 \choose 2$ * $3 \choose 1$ divided by 70?