Oh no! Matrices

Probability Level 3

How many different matrices can be formed by using 12 different elements(once each)?

The order of the matrix need not be the same.

1 solution

Krishna Sharma
Oct 2, 2014

Matrices are of the form

$m \times n$

Here are 6 possibilities (all elements using at a time)

$1 \times 12$

$2 \times 6$

$3 \times 4$

$4 \times 3$

$6 \times 2$

$12 \times 1$

And there are 12 different elements

So they can be arranged in

$12!$ ways for each matrice

Hence the answer is

$6 \times (12!) = \boxed{2874009600}$