Q168 / 269 · NDA 2025 (Phase 1) · Mathematics
What is the number of positive integer solutions of $x + y + z = 5$?
- A$3$
- B$5$
- Correct answerC$6$
- D$9$
Solution
The number of positive integer solutions to the equation $x_1 + x_2 + \dots + x_r = n$ is given by $^{n-1}C_{r-1}$.
For the given equation $x + y + z = 5$, we have $n = 5$ and $r = 3$.
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: $6$
For the given equation $x + y + z = 5$, we have $n = 5$ and $r = 3$.
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: $6$
Hence, the correct answer is option: 'C'.