COMEDK · Maths · 36. Probability
From the set \(\{1,2,3,4,5\}\) two numbers ' \(a\) ' and ' \(b\) ' \((a \neq b)\) are chosen at random. The probability that \(\dfrac{a}{b}\) is an integer is
- A \(\dfrac{1}{3}\)
- B \(\dfrac{1}{2}\)
- C \(\dfrac{3}{5}\)
- D \(\dfrac{1}{4}\)
Answer & Solution
Correct Answer
(D) \(\dfrac{1}{4}\)
Step-by-step Solution
Detailed explanation
The total number of ways to choose two distinct numbers \(a\) and \(b\) from the set \(\{1, 2, 3, 4, 5\}\) is given by the number of permutations \(^{5}P_{2} = 5 \times 4 = 20\). We need to find the number of pairs \((a, b)\) such that \(\dfrac{a}{b}\) is an integer. This means…
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