A teacher is assigning 32 presentation topics to 8 students at random. Each student will get 3 topics, and
no topic will be repeated. Somil is very interested in 5 topics. What is the probability that Somil will be
assigned at least one of his preferred topics? Complete the explanation on how you arrived at your
answer.
Somil being assigned at least one of his preferred topics is the complement of Somil being assigned
none of his preferred topics. Calculate the probability of this first, since it is easier. The sample space
n (S) is the number of combinations of 3 presentation topics Somil could be assigned which is
Somil is not very interested in topics. The event space n (A) is the number of combinations of 3
topics in which Somil is not very interested which is
The probability that Somil is not assigned any of his preferred topics is -
Thus the probability that Somil is assigned at least one of his preferred topics is —
992