As a continuation of my introduction to Combinations and Permutations, here are some practice problems to test the strategies I demonstrated. Also, I am trying out a new format. Instead of giving you practice problems and then writing out a half-page description for each one, I am simply going to give you the questions. But don’t worry – I am not leaving you in the lurch. For explanations, I am solving each of the questions – using my special approach, of course – in the video below.

Questions:

1. A committee is composed of a president, a vice president, and a treasurer. If six people are trying out for the three positions, how many different committees result?

(A) 20 (B) 40 (C) 60 (D) 105 (E) 120

2. A committee of three is to be chosen from six. How many unique committees result?

(A) 20 (B) 40 (C) 60 (D) 105 (E) 120

3. A committee is composed of a president, a vice president, and a treasurer. If five people are running for president, six people are running for vice president, and three are running for treasurer, how many unique committees result?

(A) 15 (B) 45 (C) 75 (D) 90 (E) 120

4. A jousting tournament requires that a team consist of two knights and two squires. The Merry Band is forming a team from five knights and three squires. How many different lineups can The Merry Band field?

(A) 10 (B) 13 (C) 15 (D) 30 (E) 120

5. A septet, a group composed of seven players, is made up of four strings and three woodwind instruments. If seven students try out for strings and seven different students try out for woodwinds, how many unique septets can result?

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