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

is there another way you can explain it whoever wrote that question thats horrible

the answer   is 200

step-by-step explanation:

this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )

answer is x<