Question

Let a set A = {a₁, a, a, ... a₁₈₀). Then total number of possible matrices of different order formed by using all element of set A exactly once in a matrix is n₁ (n₂!), where n₁, n₂ € N. Then least value of (n₁+ n₂) is​

Answer 1

First we have to find out what are the different orders of matrices that can be formed by 180 elements.

Totally there are 180 elements mxn be order.

180 can be formed by product of there : 

1 x 180 , 2 x 90 , 3 x 60 , 4 x 45 , 5 x 36 , 6 x 30 , 9 x 20 , 10 x 18 , 12 x 15 and it's reverse.

Total number of possible matrices orders = 9 x 2 = 18

we have 180 slots and arrange the elements in 180 elements, so We can 18 x 180! ways

Total matrices = 18 x 180! given n₁.(n₂!)

_n1 = 18, n₂ = 180

Hence, n₁ + n₂ = 18 + 180 = 198