The sum of the digits of the number of positive integral solutions satisfying the equation x1+x2+x3y1+y2=77

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answer is 6.

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Detailed Solution

x1+x2+x3y1+y2=11×7 or 7×11 In the first case, x1+x2+x3=11 and y1+y2=7, which have 10C2⋅6C1 solutions In the second case, x1+x2+x3=7 and y1+y2=11, which have 6C2⋅10C1 solutions ∴ Total number of solutions =10C2⋅6C1+6C2⋅10C1 =270+150=420

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