Find the number of natural number solutions of x1+x2+x3+3x4=15.

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Question

Find the number of natural number solutions of

x_{1} + x_{2} + x_{3} + 3 x_{4} = 15

.

Answer: Option B
:
B

\begin{matrix} X_{1} & X_{2} & X_{3} & 3 X_{4} & = 15 Case 1: & X_{1} & X_{2} & X_{3} & 3 & = 15 Case 2: & X_{1} & X_{2} & X_{3} & 6 & = 15 Case 3: & X_{1} & X_{2} & X_{3} & 9 & = 15 Case 4: & X_{1} & X_{2} & X_{3} & 12 & = 15 \end{matrix}

Case 1:

X_{1} + X_{2} + X_{3} = 12;

Total number of natural number solution =

^{11} C_{2} = 55

Case 2:

X_{1} + X_{2} + X_{3} = 9;

Total number of natural number solution =

^{8} C_{2} = 28

Case 3:

X_{1} + X_{2} + X_{3} = 6;

Total number of natural number solution =

^{5} C_{2} = 10

Case 4:

X_{1} + X_{2} + X_{3} = 3;

Total number of natural number solution = 1
Total number of natural number solution = 55 + 28 + 10 + 1 = 94

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