JEE Main 2026 · 4 Apr · Shift 2 · Mathematics Q21

← JEE Main 2026 · 4 Apr · Shift 2

MathematicsInteger+4 / -1Question 21 of 75

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 $\dfrac ab$ , where $a,b\in\mathbb N$ and $\gcd(a,b)=1$ , then $a+b$ is equal to ________.

Your answer

Answer and worked solution

Official answer: 944

Favourable choices. An increasing A.P. of dates is fixed by its first term and common difference $d\ge1$ : $\displaystyle\sum_{d=1}^{15}(31-2d)=225$ choices.

Total. $\binom{31}3=4495$ .

Probability $\frac{225}{4495}=\frac{45}{899}$ , so $a+b=944$ .

Answer: 944

Topics:Classical probability Arithmetic progression

← Previous question Next question →

JEE Main 2026 · 4 Apr · Shift 2, Mathematics question 21