Find the number of integral solutions to |x| + |y| + |z| = 15.

Options:

A . 900

B . 901

C . 902

D . 903

E . none of these

Answer: Option C : C option c Case 1:When none of them are zero Number of +ve integral solutions of x + y + z = 15 is 14C2however, x y z can be -ve also total 8 ways for each set of x y z Total 14C2×8=728 Case 2:When one of them is zero No of solutions = 3×4×14C1=168Case 3: When two of them are zeroes Number of solutions = 3×2=6 Total= 902, option (c)

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