Six different numbers are to be the elements of a matrix, each used exactly once. How many such matrices, of any order, can be formed?

Explanation

1. 01

   A matrix with 6 elements has order 1 × 6, 2 × 3, 3 × 2 or 6 × 1: 4 orders.

2. 02

   For each order, the six numbers can be arranged in $6! = 720$ ways.

3. 03

   So there are $4 \times 720 = 2{,}880$ matrices.