Over the years, as the math section has become more difficult, permutations and combinations are popping up more often. At the same time, students are also becoming more adept at handling these kinds of problems (I’d hypothesize that more practice problems are available.) As a result, permutations and combinations problems are not only more common but also more difficult.

What I’ve done is come up with the kind of permutation/combination problems, you can expect to see at the 700+ level. These questions are not easy, so do not get discouraged.

In fact, the first person to get all five problems correct, before I post my video reply at the end of the week, will win a one-month subscription to Magoosh.

Good luck!

1. A committee of three must be formed from 5 women and 5 men. What is the probability that the committee will be exclusive to one gender?

(A) 1/60

(B) 1/120

(C) 1/8

(D) 1/6

(E) 1/3

2. A three-letter code is formed using the letters A-L, such that no letter is used more than once. What is the probability that the code will have a string of three consecutive letters (e.g. A-B-C, F-E-D)?

(A) 1/55

(B) 1/66

(C) 2/17

(D) 1/110

(E) 2/55

3. A homework assignment calls for students to write 5 sentences using a total of 10 vocabulary words. If each sentence must use two words and no words can be used more than once, then how many different ways can a student select the words?

(A) 10!/5!

(B) 10!/32

(C) 5! x 5!

(D) 2! x 5!

(E) 10!

4. Team S is to comprise of n debaters chosen from x people? Team R is comprised of n + 1 debaters chosen from x+1 people.

Column A

Number of unique team S

Column B

Number of unique Team R

5. A lunar mission is made up of x astronauts and is formed from a total of 12 astronauts. A day before the launch the commander of the program decides to add p astronauts to the mission. If the total number of possible lunar missions remain unchanged after the commander’s decision, then which of the following cannot be the value of p?

(A) x

(B) x + 3

(C) 3

(D) 6

(E) 8

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