JEE Mains · Maths · STD 11 - 14. probability
From a month of \(31\) days, \(3\) different dates are selected at random. If the probability that these dates are in an increasing A.P. is equal to \(\dfrac{a}{b}\), where \(a,b \in \mathbb{N}\) and \(\gcd(a,b)=1\), then \(a+b\) is equal to ______
- A 941
- B 942
- C 943
- D 944
Answer & Solution
Correct Answer
(D) 944
Step-by-step Solution
Detailed explanation
The total number of ways to select \(3\) different dates from a month of \(31\) days is given by choosing \(3\) days out of \(31\): \(^{31}C_{3} = \dfrac{31 \times 30 \times 29}{3 \times 2 \times 1} = 4495\) Let the three selected dates be \(x, y, z\) such that \(x < y < z\).…
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