The problem asks to find the total number of 4-digit numbers that can be formed using all the digits of the number 4219.

1. Problem Description

The problem asks to find the total number of 4-digit numbers that can be formed using all the digits of the number

4

2

1

9.

2. Solution Steps

The digits we have are 4, 2, 1, and

9. We need to form 4-digit numbers using each of these digits exactly once.

This is a permutation problem. The number of ways to arrange $n$ distinct objects is $n!$.

In this case, $n=4$, so we need to find $4!$.

$4! = 4 \times 3 \times 2 \times 1 = 24$

3. Final Answer

24