First slide

Permutations

Question

The number of different matrices that can be formed with elements 0, 1 , 2 or 3, each matrix having 4 elements, is

Moderate

A

$3 x 2^{4}$
B

$2 x 4^{4}$
C

$3 x 4^{4}$
D

none of these

Solution

A matrix having 4 elements can be of the order
$1 x 4 o r 4 x 1 o r, 2 x 2 .$ Since each element can take 4 values viz
$0, 1, 2, 3 .$
$∴$ Number of different matrices of order $1 x 4$ is equal to
$4 \times 4 \times 4 \times 4 = 4^{4}$
Similarly, number of matrices of each order is $4^{4}$ .
Hence, required number of matrices $= 4^{4} + 4^{4} + 4^{4} = 3 \times 4^{4}$ .

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