If two sections of strengths 30 and 45 are formed from 75 students who are admitted in a school, then the probability that two particular students are always together in the same section is

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Aicharya · Accepted Answer

According to given informations, the required probability $\begin{aligned} & =\frac{{ }^{73} C_{28}+{ }^{73} C_{43}}{{ }^{75} C_{30}} \ & =\frac{\frac{73 !}{28 ! 45 !}+\frac{73 !}{43 ! 30 !}}{\frac{75 !}{30 ! 45 !}} \ & =\frac{\frac{1}{45 \times 44}+\frac{1}{30 \times 29}}{\frac{75 \times 74}{(30 \times 29)(45 \times 44)}} \ & =\frac{(30 \times 29)+(44 \times 45)}{(75 \times 74)} \ \end{aligned}$ $\begin{aligned} & =\frac{(2 \times 29)+(44 \times 3)}{(5 \times 74)}=\frac{29+(22 \times 3)}{5 \times 37} \ & =\frac{29+66}{5 \times 37}=\frac{95}{5 \times 37}=\frac{19}{37} \end{aligned}$ Hence, option (2) is correct.

If two sections of strengths 30 and 45 are formed from 75 students who are admitted in a school, then the…

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