Question

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

• A. $\frac{66}{185}$
• B. $\frac{19}{37}$
• C. $\frac{29}{185}$
• D. $\frac{18}{37}$

Answer 1

Answer: (B)

$\frac{19}{37}$

Answer 2

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