Question

A matrix of order 3 $\times$ 3 is formed by using the elements from {1, 2, ------, 9} without repetition. Then

• A. The probability that first row has entries in increasing order is 1/6
• B. The probability that first row and first column are in increasing order is 1/20
• C. The probability that first row and first column are in increasing order and given that the last element of 3^rd row and 3^rd column is the greatest is 1/20
• D. Probability that first row in increasing order given that second and third rows are in increasing order is 1/6

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A

The probability that first row has entries in increasing order is 1/6

B

The probability that first row and first column are in increasing order is 1/20

C

The probability that first row and first column are in increasing order and given that the last element of 3^rd row and 3^rd column is the greatest is 1/20

D

Probability that first row in increasing order given that second and third rows are in increasing order is 1/6

$\left(A\right)\frac{{}^9{C}_3-6!}{9!}=\frac{1}{6}\left(B\right)\frac{{}^9{C}_5{-}^4{C}_2-4!}{9!}=\frac{1}{20}\left(C\right)\frac{{}^8{C}_3{-}^4{C}_2\times 3!}{8!}=\frac{1}{20}\left(D\right)\frac{1}{3!}=\frac{1}{6}$