Three numbers chosen without replacement from 1,,8.

Question

Three numbers chosen without replacement from $\{1,\dots,8\}$. Find $P(	ext{min}=3\mid	ext{max}=6)$.

Accepted Answer

Given max$=6$, the third number is chosen from $\{4,5\}$ or must be $\ge3$; specifically:

$$P(\min=3\mid\max=6) = \frac{{}^2C_1}{{}^5C_2}=\frac{2}{10}=\frac15$$

Solutions · 1