Question:medium
From the first 100 natural numbers, two numbers first \( a \) and then \( b \) are selected randomly without replacement. If the probability that \( a - b \ge 10 \) is \( m/n \), \( \text{gcd}(m, n) = 1 \), then \( m + n \) is equal to :
From the first 100 natural numbers, two numbers first \( a \) and then \( b \) are selected randomly without replacement. If the probability that \( a - b \ge 10 \) is \( m/n \), \( \text{gcd}(m, n) = 1 \), then \( m + n \) is equal to :
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For "without replacement" problems where order matters (first \(a\), then \(b\)), the total sample space is $n(n-1)$. If order didn't matter, it would be $^nC_2$.
Updated On: Feb 24, 2026
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Correct Answer: 311
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