The number of non-negative integral solutions to the system of equations x + y + z + u + t = 20 and x + y + z = 5 is

detailed solution

Correct option is A

Given, x + y + z + u + t = 20               (1)x + y + z = 5                                        (2)Given, system of equations is equivalent tox + y + z = 5                                       (3)and, u + t = 15                                    (4)Number of non-negative integral solutions of equation (3)=n+r−1Cr=3+5−1C5=7C5,Number of non-negative integral solutions of equation (4)=n+r−1Cr=2+15−1C15=16C15∴ Required number =7C5×16C15=336.