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

2) How many four-digit numbers are there in which all four digits are unique (in other words, no digits repeat)? For example, 3212 would NOT be such a number because the 2 repeats.

(A) 4,536

(B) 4,698

(C) 5,760

(D) 8,019

(E) 9,000

3) The five members of the boys fencing team – Alan, Bailey, Craig, David and Edward – are having their photo taken for the yearbook. They will sit in five chairs that are arranged side by side in a row. However, Bailey and Edward have a phobia that keeps them from being on the end of a row. In how many ways can the team members arrange themselves for the photo?

(A) 6

(B) 12

(C) 24

(D) 36

(E) 60

4) There are 6 students in Grade 7 and 4 students in Grade 8 who are interested in serving on the Principal’s Advisory Committee. The principal has determined that she will choose 2 students in Grade 8 and 1 student in Grade 7 for this committee. How many different groups of three students are possible?

(A) 24

(B) 30

(C) 32

(D) 36

(E) 48

5) At a business meeting, each of the five participants shakes hands with everyone else at the meeting. How many handshakes are there all together?

(A) 8

(B) 10

(C) 12

(D) 16

(E) 20

6) John is going to choose two of the four cards below at random and will then add the value of the two cards. How many different sums are possible?

(A) 4

(B) 5

(C) 6

(D) 8

(E) 12

If you have questions about these problems, the “Listing and Counting” techniques, or anything else to do with the SAT, leave a comment or send me an email at info@cardinalec.com .

If you want some more practice on Listing and Counting problems, you can find our first set of these problems here.

Solutions:

1) (C)

2) (A)

3) (D)

4) (D)

5) (B)

6) (B)