Question 43 — JEE Main 22 Jan 2026 (S I)

Solution

First Method:

$\mathrm{P}(\mathrm{ab}$ is divisible by 3$)$
$=\mathrm{P}(\mathrm{a} \& \mathrm{~b}$ both are multiple of 3$)+\mathrm{P}($ Exactly are of $\mathrm{a} \& \mathrm{~b}$ is multiple of 3$)$
$=\frac{{ }^{16} \mathrm{C}_{2}}{{ }^{50} \mathrm{C}_{2}}+\frac{{ }^{16} \mathrm{C}_{1} \times{ }^{34} \mathrm{C}_{1}}{{ }^{50} \mathrm{C}_{2}}=\frac{8.15+16.34}{25(49)}=\frac{664}{1225}$
$3 \mathrm{~K}=\{3,6,9, \ldots, 48\}$

Second Method:

Number which are not multiple of $3=50-16=34$
$\mathrm{P}(\mathrm{ab}$ is divisible by 3$)=1-\mathrm{P}(\mathrm{ab}$ is not divisible by 3$)$
$=1-\frac{{ }^{34} \mathrm{C}_{2}}{{ }^{50} \mathrm{C}_{2}}=1-\frac{17 \times 93}{25 \times 49}=\frac{1225-561}{1225}=\frac{664}{1225}$ Answer(2)