Problem:
Ms. Carr asks her students to read any of the books on a reading list. Harold randomly selects books from this list, and Betty does the same. What is the probability that there are exactly books that they both select?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
We don't care about which books Harold selects. We just care that Betty picks books from Harold's list and that aren't on Harold's list. The total amount of combinations of books that Betty can select is
There are
ways for Betty to choose of the books that are on Harold's list. From the remaining books that aren't on Harold's list, there are
ways to choose of them.
We can analyze this as two containers with balls each, with the two people grabbing balls each. First, we need to find the probability of two of the balls being the same among five:
After that, we must multiply this probability by
for choosing the balls that are the same chosen among balls. The answer will be
The problems on this page are the property of the MAA's American Mathematics Competitions