N = {Alan, Bill, Cathy, David, Evelyn} Assuming that all members are eligible, but no one can hold more than one office, list and count the different ways the club could elect each group of officers. 1. A president, a secretary, and a treasurer, if the president must be a man and the other two must be women. 2. (a) How many two digit numbers can you make with {2,3,5,7} (b) out of the two digit numbers you were able to come up with, which ones are even numbers? (c) out of the two digit numbers you were able to come up with, which ones are multiples of 3? 3. Construct a tree diagram showing all possible results when three fair coins are tossed. Then list the ways of getting each result (a) at least two heads (b) more than two heads (c) no more than two heads (d) fewer than two heads (part 2) 1. 50! __________ 48! * 2! 2. 19! __________ 9! * 10! 3. n! ___________ r!(n-r)! where n = 26 and r = 20 Find the number of distinguishable arrangements of the letters of this phrase. 4. VICE VERSA 5. When two dice are rolled. How many outcomes would there be if three fair dice were rolled. Determine the number of different possibilities for the type of number described. 6 . Odd three-digit numbers Determine the number of possible ways to mark your answer sheet for this test scenario. 7. A ten-question multiple-choice test with five answer choices for each