Probability of number of question to appear in exam.

Question

An examiner sets a question paper with 10 questions out of 50 different questions available. Out of these 10, a student has to attempt to answer only 1 question. A student 'ABC' prepared only 10 questions of these 50. What is the probability that he gets at least one question (of the 10 set by the examiner) to be from the questions prepared by him?

Answer 1

There are 50 questions $x = \{x_1, x_2,..x_{50}\}$. No of ways to choose 10 questions is $\binom{50}{10}$. Let say the students prepared for 10 questions $\in x$. No of ways to choose 10 questions out of remaining 40 is $\binom{40}{10}$. These 10 questions contain none of the questions prepared by the student. Now the probability that the at least one student's question appears in the question paper is \begin{equation} 1-\frac{\binom{40}{10}}{\binom{50}{10}} \end{equation}