What is the number of positive integer solutions of x + y + z = 5 ?

Question

Quantrex Academy · Accepted Answer

Correct answer: C. 6

The number of positive integer solutions to the equation

x_1 + x_2 + \dots + x_r = n

is given by ^{n-1}C_{r-1}

.<br><br>For the given equation

x + y + z = 5

, we have

n = 5

and

r = 3

.<br><br>The number of positive integer solutions is ^{5-1}C_{3-1} = ^{4}C_{2}

.

^{4}C_{2} =

\dfrac{4 \times 3}{2 \times 1} =6

.

Answer: 6

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