Kenneth Rosen Edition 7 Exercise 6.5 Question 39 (Page No. 433)

Question

How many ways are there to travel in $xyz$ space from the origin $(0, 0, 0)$ to the point $(4, 3, 5)$ by taking steps one unit in the positive $x$ direction, one unit in the positive $y$ direction, or one unit in the positive $z$ direction? (Moving in the negative $x, y,\: \text{or}\: z$ direction is prohibited, so that no backtracking is allowed.)

Answer 1

we can choose x direction movement by 4 ways as the movementis unit step wise.

similarlry y direction movement can be done in 3 ways and Z direction movemment can be done in 5 ways.

hence total nos of ways to travel is 4*3*5=60 ways