Question

Out of a group of $8$ highly qualified doctors in hospital, $6$ are very kind and cooperative with their patients and so are very popular, while the other two remain reserved. For a health camp, three doctors are selected at random. Find the probability of the number of very popular doctors.

Answer 1

$8$ doctor $\Rightarrow$6 $ kind, good one

$2$ reserved

$3$ doctor sector

$=\frac{{}^6{C}_3}{{}^8{C}_3}$

$\frac{\frac{6\times 5\times 4\times 3!}{3!\times 3!}}{\frac{8\times 7\times 6\times 5!}{5!\times 3!}}\Rightarrow \frac{6\times 5\times 4}{8\times 7\times 6}$

$=5/14$