The call signs of radio and television stations in the United States generally begin with the letter W east of the Mississippi River and the letter K west of the Mississippi. Repetition of letters is allowed. How many different call signs are possible if each station uses a W or K followed by 3 letters?

The figure above represents four offices that will be

assigned randomly to four employees, one employee

per office. If Karen and Tina are two of the four

employees, what is the probability that each will be

assigned an office indicated with an X ?

The figure is Four boxes or (offices) and two of them are labeled X.

In a post I read of yours you said that with the exception of 3 things (lines, ……) there are no other formulas you should memorise. In other posts of your I have seen you use the combinations formula. What are your thoughts on using the permutations and combinations formula ?

Could you point me in the direction of any posts you have made (or section in your book) where you discuss counting problems specifically.

Thanks man

Carmen arranges stacks of blocks so that each successive level has 1 fewer block then the level below it and the top level has 1 block. Carmen wants to make such a stack with 12 levels. how many blocks does she need?

Ten distinct lines lie in the same plane. No pair of these lines is parallel to each other, and no more than two of the lines intersect at any one point. How many points lie on more than one of these ten lines? A)10 B)36 C)45 D)55 E)100

How’s everyone else doing on this quiz?

* I don’t advocate violence towards cats (or other animals). “There’s more than one way to skin a cat” is a phrase that I used to hear all the time growing up, but that I now realize (having received some mortified stares at its utterance) that it’s not as common as I thought it was. (more…)

Source. One technique-able counting problem type that you might come across on the SAT is what I’ll call a “possibilities” problem*. It might involve cards (but not playing cards – the SAT doesn’t like those), or pictures being lined up on a wall in different orders. Your job will be to determine the number of (more…)

An unfortunate truth about the SAT is that while many questions can be answered with snappy tricks (many of which can be found on these pages), not all of them can. Most “counting” questions (and probability questions, for that matter) fall into this category. Yes, I’m serious. Most. Basically, if you don’t see within 15 (more…)

This Labor Day weekend I’m going to the wedding of one of my oldest friends from my hometown. Combine the fact that the number of my friends who aren’t married is dwindling dangerously close to zero and the fact that I wasn’t able to attend this year’s fantasy football draft so I had to autodraft (more…)

The SAT will throw two common kinds of “counting” problems your way. I’ll handle one of them in this post. The other kind, well, I’ll get to it when I get to it. 🙂 I like to call this kind of problem a matching problem. It’ll usually involve a bunch of people who all need (more…)

I lifted a box that was too heavy this week and I screwed up my back so bad that every time I put weight on my right foot, searing pain shoots up my entire right side. Getting older is awesome! The prize this week for the first correct response: FREE Beta Access to my book. (more…)