Home › Previous year questions › GATE 2010 CS (CS1) › Question 37GATE 2010 CS (CS1) – Question 37 Engineering Mathematics · Discrete Mathematics: Combinatorics (Counting, Recurrence Relations, Generating Functions) · 2 marks · Multiple choice
A divisor of $10^{99}$ is chosen uniformly at random. What is the probability that it is a multiple of $10^{96}$?
1/625 4/625 12/625 16/625 Practise this question in The GATE Grind →
Show answer and explanation Correct answer: (A) 1/625
Explanation Every divisor is $2^a5^b$, with a,b independently ranging from zero through ninety-nine, giving 10000 divisors. Divisibility by $10^{96}$ requires both exponents to be at least ninety-six. There are four choices for each, giving sixteen favourable divisors. Thus 16/10000=1/625, A.
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