Introduction to Discrete Math

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) 3