Q19 / 54 · JEE Advanced 2017 (Paper 2) · Mathematics

Three randomly chosen non negative integers $x, y, z$ are found to satisfy the equation $x + y + z = 10$ . Then the probability that $z$ is even, is

Solution

Let $z = 2 k,$ where $k = 0, 1, 2, 3, 4, 5$

$∴ x + y = 10 - 2 k$

Number of non negative integral solutions

$\sum_{k = 0}^{5}^{11 - 2 k} C_{1} = \sum 11 - 2 k = 36$

Total cases $=^{10 + 3 - 1} C_{3 - 1} = 66$

Required probability $= \frac{36}{66} = \frac{6}{11}$

Hence, the correct answer is option: 'B'.