Committee with Order: Probability that Person A is chosen as president or treasurer Question: There are 20 people to be selected for a committee of three, consisting of a president, secretary general and a treasurer. What is the probability that a particular Person $A$ will be selected as president **or** treasurer? Could you please verify my answer? ${^{19} P_2\over ^{20} P_3}=0.05$ I'm not sure if there is supposed to be some form of adding two permutations in the answer?

Let $P$ denote the event that person A is chosen for president and let $T$ denote the event that person A is chosen for treasurer.

Then the events $P$ and $T$ are mutually exclusive so that:$$\Pr(P\cup T)=\Pr(P)+\Pr(T)=\frac1{20}+\frac1{20}=0.1$$