Let A= (a,b,c): a,b,c are non-negative integers and a+b+2c=22 . Then n(A) is equal to:

Step-by-step solution

The given equation is a + b + 2c = 22 , where a, b, c are non-negative integers. This can be rewritten as a + b = 22 - 2c . Since a 0 and b 0 , we must have 22 - 2c 0 , which gives c 11 . Since c is a non-negative integer, the possible values for c are 0, 1, 2, , 11 . For a fixed value of c , the number of non-negative integer solutions to the equation a + b = 22 - 2c is given by (22 - 2c) + 1 = 23 - 2c . The total number of solutions n(A) is the sum of the number of solutions for each possible value of c : n(A) =