EXAMPLE 1.5.23 SOLUTIONS

Is it P(9,5), C(9,5) or 9⁵?

Each item below can be answered with either A. P(9,5); B. C(9,5); or C. 9⁵

Choose the correct answer in each case.

1. The number of 5-element subsets in a 9-element set = C(9,5)

2. The number of 5-symbol codes that can be formed using the symbols

{@, /, $,À, &, §, £, Ω, ? } if repeated symbols are allowed = 9⁵

3. The number of different ways to choose 5 people from a set of 9 and position them in 5 seats = P(9,5)

4. The number of ways to choose a chairperson, associate chairperson, parliamentarian, treasurer, and secretary from a list of 9 candidates = P(9,5) (assuming that no person will hold more than one office).

5. The number of different 5-person groups that can be chosen from a collection of 9 people = C(9,5)

6. The number of 4-element subsets in a 9-element set = C(9,4), which is the same as C(9,5)