Taxi route counts #6

Geometry Level 3

$d=4$ and $\vec{V}=(4,4,4,4)$ , where $n$ is a positive integer.

There are a positive integer number, $d$ , of independent vectors, $\vec{V}_i$ , where $i$ runs from 1 to $d$ . A trip starts from the appropriate $\vec{0}$ of $d$ components and goes to a destination vector of $d$ positive integer components. A step of a trip consists of adding $1$ to a single component of the taxi's current position vector which was initially $\vec{0}$ of $d$ components. How many distinct routes would accomplish this trip?

The answer is 63063000.

1 solution

A Former Brilliant Member
Nov 30, 2019

If you have done the previous problems in this series and have been paying attention or already know the method of solution then, you will realize that the answer is $\frac{16!}{(4!)^4}$ or $63063000$ .

Multinomial of $\vec{V}$ is $\frac{(\sum_{i\in \vec{V}}{i})!}{\prod_{i\in \vec{V}}{i!}}$

Multinomial $((4,4,4,4))=\frac{16!}{(4!)^4}=63063000$

Taxi route counts #6

The answer is 63063000.

1 solution

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