How many solutions are there to the equation x1 + x2 + x3 + x4 = 17, where x1, x2, x3, x4 are nonnegative integers? (A) 1140  (B) 1160  (C) 1040  (D) 1200  No Links 

Dear Student,

Here given X1+X2+X3+X4=17

Consider the equation is A+B+C+D=X

Then the formula of finding numbers of possible non-negative integers solution is (X+4–1) C (4–1) [there are 4 numbers A, B, C, D]

SO The formula is 17+4-1 C 4–1=20C3 = 1140 (option A)

So 20C3 is the number of possible non-negative integers.


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