The total number of points is 13. Your total score will be divided by 13 to produce a score over 100. Show all work.
You don’t need to compute an exact answer. Number-only answers will be ignored.
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)