How many solutions are there for the equation A+B+3C = 10 if A,B,C are whole numbers?

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Solution

The correct option is D 26
Option (d)

It is given that A,B and C can take values ≥0

Give values to C from 0

At C=0, the equation changes to A+B=10. Number of solutions will be based on

arrangement of 10 zeroes and 1 one = $^{11} C_{1}$ = 11

At C=1, the equation changes to A+B=7. Number of solutions= $^{8} C_{1}$ =8

At C=2, the equation changes to A+B=4. Number of solutions= $^{5} C_{1}$ =5

At C=3, the equation changes to A+B=1. Number of solutions= $^{2} C_{1}$ =2

Total number of solutions = 11+8+5+2 = 26

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