# Fundamental Counting Principles: Permutation & Combination

1.) A club with 10 members is to pick a president, vice president, treasurer, and secretary. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled?

2.) Find the value of the following expression:

a. 12P4

b. 12C4

c. 4P4

d. 10P8

e. 10C8

3.) A test has 10 true/false questions. How many different tests can be turned in to the teacher?

4.) A car is available in three types of models and in three types of colors. In how many combination can you buy the car?

5.) In how many ways can you make a four letter password from A, B, C, D and E if you are not allowed to repeat characters?

6.) In how many ways can you choose 7 cards from a deck of 52 cards?

7.) Use the fundamental counting principle to solve:

How many different four-letter radio stations call letters can be formed if the first letter must be W or K?

8.) Use the formula for C to solve:

A four person committee is to be elected from an organization's membership of 11 people. How many different committees are possible?

Please see the attached document for questions.

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#### Solution Preview

Please see the attachment for response.

1.) A club with 10 members is to pick a president, vice president, treasurer, and secretary. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled?

Answer

There are 10 ways to pick a president, 9 ways to pick a vice president, 8 ways to pick a treasurer and 7 ways to pick a secretary.

Therefore, total number ways to fill the office = 10 * 9 * 8 * 7

= 5040

[In other words, total number ways to fill the office = 10P4

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#### Solution Summary

The solution provides step by step method for the calculation of number of different ways and arrangements using the principles of permutation and combination. Formula for the calculation is also included.