JEE MAIN - Mathematics (2025 - 2nd April Morning Shift - No. 21)
Three distinct numbers are selected randomly from the set $\{1,2,3, \ldots, 40\}$. If the probability, that the selected numbers are in an increasing G.P., is $\frac{m}{n}, \operatorname{gcd}(m, n)=1$, then $m+n$ is equal to __________ .
Answer
2477
Explanation
| Common ratio | Last triplet | Total |
|---|---|---|
| r = 2 | 10, 20, 40 | 10 |
| r = 3 | 4, 12, 36 | 4 |
| r = 4 | 2, 8, 32 | 2 |
| r = 5 | 1, 5, 25 | 1 |
| r = 6 | 1, 6, 36 | 1 |
| Total = 18 | ||
Total choices $={ }^{40} C_3=9880$
$$\begin{aligned} & \text { Required probability }=\frac{18}{9880}=\frac{9}{4940}=\frac{m}{n} \\ & m+n=4949 \end{aligned}$$
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