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Combinatorics: Prerequisite Check

We teach hard concepts with the easiest words we can. Let's make sure you know the words and ideas we need. This course is just right if you get at least 80% on this test, but less than 70% of the place-out test. This test should be very easy for you, since it is only making sure you have the basics to understand.

Time Left:



If \(a = 2^b c\) and \(b = 3\) and \(c = 5,\) what is \(A?\)








\[\frac{6 \times 5 \times 4}{3 \times 2 \times 1}\]

\(\displaystyle \frac{5}{2}\)






All but one of these rings of 6 beads can be obtained from the others by rotating or flipping over the ring. Which is the unusual one?


When buying a certain model of phone, there are \(3\) colors to choose from, and \(3\) different amounts of storage to choose from. How many different combinations are there for that phone model?







Jenny has \(3\) skirts, \(2\) pants, and \(4\) shirts. How many ways can she create an outfit with one of the shirts, and either a skirt or pant?







Everybody in a certain middle school takes French, Spanish, or both. The French teacher has a total of \(90\) students, and the Spanish teacher has a total of \(110\) students. There are \(20\) students in both languages. How many students are at the school?