Tag Archives: counting

SAT Math: More Listing and Counting Problems

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Last year, we wrote a post about Listing and Counting problems.  This type of problem isn’t as common as those that deal with functions or special right triangles, but if you want to maximize your score, you should know how to do these.

Below are six more problems that will give you some practice on these problems.  The answers appear at the bottom of this post.

1)  Three identical candy bars were distributed between Alice, Brad and Carl.  There was no guarantee that each of them would get a candy bar (in other words, one or more of them could have gotten no candy bars at all).  If Alice got at least one candy bar, in how many ways could the candy bars have been distributed?

(A)  4
(B)  5
(C)  6
(D)  8
(E)  12

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SAT Math: More Listing and Counting Problems

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If you’ve read my recent post on Listing and Counting and you’re looking for some more practice on this type of SAT Math problem, here are a few more examples you can try.  The answers appear at the bottom of this post.

1)  Six points are drawn on a circle.  How many triangles can be drawn by connecting any three of these points?

(A)  12
(B)  20
(C)  30
(D)  60
(E)  120

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SAT Math: Listing and Counting

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Problems that ask you to determine in how many ways something can happen are generally called permutation and combination problems.  They are not as common on the SAT as, say, function problems, but if you are looking to maximize your math score, it would be helpful to master these types of problems.  You are likely to run into one or two of them, and when you do they are usually near the end of a section among the harder problems.

Permutations are problems in which order matters.  For instance, if you are asked to determine in how many ways a group of students can line up, that is a permutation problem.  If order does not matter, then using combinations is appropriate.  You might recall the formulas from your math class:

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