Answer
27,720
Work Step by Step
We have to go from (0,0,0) to (4,3,5). For this, we have to travel 4 times in positive x-direction, 3 times in the positive y-direction and 5 times in positive z-direction.
n = 4+3+5 = 12
k = 3
$n_{1}$= 4
$n_{2}$ = 3
$n_{3}$ = 5
Distributing n distinguishable objects into k distinguishable boxes such that $n_{i}$ objects are in each box can be done in $\frac{n!}{n_{1}!...n_{k}!}$
= $\frac{12!}{3!.4.!.5!}$ = 27,720