Posted: November 19th, 2015

Math homework

The total number of points is 13. Your total score will be divided by 13 to produce

a score over 100. Show all work.

1

A club with 17 women and 21 men needs to form a committee of size 7: (1 point each)

1. How many committees are possible?

2. How many committees are possible if a committee must have 2 women and 5 men?

3. How many committees are possible if a committee must consist of all women or all

men?

4. How many committees are possible if a committee must have at least 3 women?

1

5. How many committees are possible if a committee must have exactly one women?

6. How many committees of eight different executive positions are possible? (e.g.,

chair, treasurer, secretary, etc.)

2

In the questions below, suppose a “word” is a string of 8 letters of the alphabet

with repeated letters allowed: (1 point

each)

1. How many words are there?

2. How many words end with the letter T?

3. How many words begin with R and end with T?

4. How many words start with A or B?

2

5. How many words begin with A or end with B?

6. How many different words composed of 5 As and 3 Bs are there?

3

In how many ways can 15 distinct balls be distributed into five distinct urns if

each urn must contain at least one ball?

Explain.(1 point)

3

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