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Quiz #2: Small-Group Completion Names __________________________________

15 points (5 pts each)

Impact on Course Grade: approximately 2%-3% Score ___________

Show appropriate combinatorial evidence to fully support your solutions!

Review your responses. Do your solutions seem reasonable? Are labels included if necessary?

Solve three of these four problems. Clearly indicate the solutions I am to evaluate. If that is not

clear, I will grade the first three solutions I get to.

You are to work as a group of three to solve the problems. Each member of the group is

responsible for writing one solution. You may use no other resources.

It is not necessary to complete every calculation. That is, your responses may contain

combinatorial notation. Include explanations as justify your solution.

1. A collection of books is to be placed in line on one shelf. There are 20 green books and

there are 12 red books. The books are distinguishable only by color. (a) How many shelf

arrangements are possible for these 32 books? (b) If red books cannot be adjacent to one

another, how many shelf arrangements are possible?

2. How many even integers between 2000 and 6000, inclusive, have digits that do not

repeat?

3. A women’s community choir has 10 singers. Of those, 8 are selected to perform. Two (2)

of the 10 singers sing soprano only. One (1) of the 10 singers sings alto only. Seven (7) of

the 10 singers can sing either soprano or alto. If an 8-singer choir requires four sopranos

and four altos, how many different groups of 8 people could assemble?

4. Twenty-five (25) chess players from throughout the county compete in a weekend

tournament. At the end of competition, the top four players are awarded Gold, Red, Blue,

and White ribbons. The bottom five players must move to a less-competitive chess

league. Under these conditions, how many tournament outcomes are possible?

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