Answer
50,450,400
Work Step by Step
We have to go from (0,0,0) to (4,3,5,4). 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+4 = 16
k = 4
$n1$= 4
$n2$ = 3
$n3$ = 5
$n4$ = 4
Distributing n distinguishable objects into k distinguishable boxes such that $n_{i}$ objects are in each box can be done in $\frac{n!}{n_{1}!...n_{k}!}$
= $\frac{16!}{4!.3!.5!.4!}$ = 50,450,400