CMSC150 Introduction to Discrete Math Summer 2015 Homework 4 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 8: (1 point each) 1. How many committees are possible? 2. How many committees are possible if a committee must have 3 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 A bowl contains 53 red balls, 48 blue balls, and 72 green balls. A woman selects balls at random without looking at them. We assume that the woman does not replace the balls after drawing them. What is the least number of balls she must select to be sure of having at least 16 balls of the same color? Explain.(1 point) 3