Permutations and Combinations 1 Question 2

2. How many 3×3 matrices M with entries from 0,1,2 are there, for which the sum of the diagonal entries of MTM is 5 ?

(2017 Adv.)

(a) 198

(b) 162

(c) 126

(d) 135

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Answer:

Correct Answer: 2. (a)

Solution:

  1. Sum of diagonal entries of MTM is ai2.

i=19ai2=5

Possibilities I. 2,1,0,0,0,0,0,0,0, which gives 9!7! matrices

II. 1,1,1,1,1,0,0,0, 0 , which gives 9!4!×5! matrices

Total matrices =9×8+9×7×2=198



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