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

Question

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

Answer: Option B
:
B
It is given that A,B and C can take values ≥0
Give values to C from 0 to 3
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}

=1

Total number of solutions = 11+8+5+1 = 25

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