Let A be a matrix of order 2x2, whose entries are from the set {0, 1, 2, 3, 4, 5}. If the sum of all the entries of A is a prime number p, 2 < p < 8, then the number of such matrices A is :
Text Solution
Verified by Experts180
(180)
Let A = 
; a, b, c, d 
{0, 1, 2, 3, 4, 5}
a + b + c+d = p,p 
{3,5,7}
Case-(i)
a + b + c + d = 3;a,b, c,d 
{0, 1,2,3}
No. of ways = 3+4-1 C 4-1 = 6 C 3 = 56 ........(1)
Case-(ii)
a + b + c + d = 5;a,b,c,d 
{0,1,2,3,4,5}
No. of ways = 5+4-1 C 4-1 = 8 C 3 = 56 ........(2)
Case-(iii)
a+b+c+d=7
No. of ways = total ways when a, b, c, d 
{0, 1, 2, 3,4, 5, 6, 7}- total ways when a, b, c, d 
{6, 7}
No of ways = 
= 10 C 3 -16=104 ........(3)
Hence total no. of ways = 180
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