A probability problem. > A club has five members $A,B,C,D$ and $E$. It is required to select a chairman and secretary. Assuming that one member cannot occupy both positions, write the sample space associated with these selections . **My input** In my mind I thought of selecting two from these $5$ people first one as chairman and second one as secretary. $5$ choose $2$ makes it $10$ but order doesn't matter because first one can also b secretary and $2$nd can be chairman. Using permutation makes it $20$ possible pairs. $AB,BA,AC,CA....$ Did i think it right ?

Let $M =\\{A,B,C,D,E\\}$, then set of interest $S$ (The probability space) is as follows $$S = \\{(s,c)\in M\times M :s\
eq c\\}$$