Suppose that a computer program provides a non-negative and integer-valued…

GATE · 2026 · DA · Data Science & AI

Suppose that a computer program provides a non-negative and integer-valued random solution to the equation 𝑛1 + 𝑛2 + 𝑛3 + 𝑛4 = 20. Which of the following is the probability that all of 𝑛1,𝑛2,𝑛3,𝑛4 in the provided solution are positive?

  1. A.

    (193)(233)\frac{\binom{19}{3}}{\binom{23}{3}}

  2. B.

    (204)(244)\frac{\binom{20}{4}}{\binom{24}{4}}

  3. C.

    (203)(233)\frac{\binom{20}{3}}{\binom{23}{3}}

  4. D.

    (194)(244)\frac{\binom{19}{4}}{\binom{24}{4}}

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