Expected number of students problem? Suppose that in a class of 50 students, the instructor calls on students to answer questions,
for each question selecting one student at random and without consideration of whom he has
called on in the past. If the instructor asks 20 questions of the class, what is the expected
number of students he would have called on?
wouldn't this just be 1 + (49/50) + (48/50) until the twentieth term?
 A: Have you learned Markov Chains? It is very simple to do it using that. Assume that we have asked one question (thus identifying one unique student). 
We can define the Transition Matrix as:
\begin{align}
X=
\begin{pmatrix}
1/50 & 49/50\\
 & 2/50 & 48/50\\
 &  & \ddots\\
 &  &  & \ddots\\
 &  &  &  & 20/50
\end{pmatrix}
\end{align}
Let $P=X^{19}$. These are the number of transitions till the end of the lecture (Realize that our initial state was when we had already asked one question). 
The answer to your question can then be given by $$\sum_{i=1}^{20} i\times P_{1i}=16.6196$$
Where $P_{1i}$ implies the element in the first row and $i^{th}$ column.
A: I'm converting mjqxxxx's comment into a community wiki answer since the only existing answer is astronomical overkill for the question at hand.
The probability that a particular student is ever called on is $1−\left(\frac{49}{50}\right)^{20}$, so [by linearity of expectation] the expected number of students called on is just $50\cdot(1-\left(\frac{49}{50}\right)^{20}\approx16.62$. 
