Question

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

• A. 900
• B. 901
• C. 902
• D. 903
• E. none of these

Answer 1

The correct option is C 902

option c

Case 1:When none of them are zero

Number of +ve integral solutions of x + y + z = 15 is ${}^{14}{C}_2$ however, x y z can be -ve also total 8 ways for each set of x y z Total ${}^{14}{C}_2\times 8=728$

Case 2:When one of them is zero

No of solutions = $3\times 4{\times }^{14}{C}_1=168$ Case 3: When two of them are zeroes

Number of solutions = $3\times 2=6$

Total= 902, option (c)