Question

A matrix of order 3 × 3 is formed by using the elements {1, 2, 3, ……….9} without repetition. Number of ways in which matrix is formed if:

1. First row and first column have entries in increasing order, is

2. First row & first column have entries in increasing order such that last entry of the third row and third column is greatest, is

Answer 1

1. First row and first column have entries in increasing order, is

\(\frac{{^9C_5} - {^4C_2} - 4!}{9!} = \frac 1{20}\)

2. First row & first column have entries in increasing order such that last entry of the third row and third column is greatest, is

\(\frac{{^8C_3} - {^4C_2} \times 3!}{8!} = \frac 1{20}\)