For each problem, display the final numerical answer and the equation(s) used to form the answer. Leave combinations, permutations, factorials, and exponents intact. Good example: C(6, 3) - C(5, 2) = 10 Bad examples: 10 no equation C(6, 3) - C(5, 2) no final answer 20 - 10 = 10 did not leave combinations intact If the final equation is too complex, introduce variables and break it down into two or more equations. You are encouraged to show additional work to indicate how you derived your equation. 1. (16 points, 4 points each) ZUX is a strange person who only uses the 13 letters that comprise the second half of the alphabet (N-Z). Using just the second half of the alphabet (uppercase letters only), how many strings of seven letters are there... a. if letters cannot be repeated? b. if letters can be repeated? c. if letters cannot be repeated and the string starts with either Z, U, or X. d. if letters can be repeated and at least one of the three following conditions is true: (i) the string starts with Z. (ii) the fourth letter is U, and (iii) the string ends with X.3. (20 points, 4 points each) A bagel shop has bagels in the following six varieties: plain, sesame, onion, blueberry, asiago cheese, and everything. Assuming there 1s at least 20 bagels of each variety, how many ways are there to choose 20 bagels... with no restrictions. with at least two of each vanety. with three or fewer blueberry bagels. at least two plain bagels but no more than four plain bagels. with three or fewer blueberry bagels and three or fewer onion bagels. o a0 Te