Probability and expectancy problem if we choose a **size $25$ subset** of the set: $\\{1,2,....100\\}$ what is the expectancy of the number of sequential pairs in the subset? expectancy still confuses me, can anybody help?

Let $X_i$ be an indicator random variable that $i$ and $i+1$ ($i\in \\{1,2,...,99\\}$) are in a choosen subset.

Then $$ P(X_i = 1) = {{98\choose 23}\over {100\choose 25}}= {6\over 99}$$ Since $X= X_1+...+X_{99}$ we have $$ E(X) = E(X_1)+...+E(X_{99}) = 99{6\over 99} = 6$$