1. A salesman has eight shirts, 4 suits and 10 ties. How many different combinations of a suit with a shirt and a tie can he wear? 2. There are four different routes connecting city A to city B. In how many ways can a round trip be made from A to B and back? 3. A businessman is planning to go from New York to Chicago with one stop-over at Pittsburgh. He has a choice of a plane, a train, or a bus from New York and a choice of train or bus from Pittsburgh. Draw a tree diagram indicating the different choices for making a complete trip to Chicago? 4. From the digits 2,3,4,5,6 and 7, a two-digit numeral is formed so that no digit is repeated. How many such numerals are possible? Of these, how many are even numbers? 5. The nominations for officers of the mathematics association of Ethiopia consist of five candidates and three are to be elected. In how many ways can a president, Secretary, and treasurer be elected? 6. In how many ways can five students be seated in a classroom with 20 disks? 7. How many three-digit numerals can be formed from the digits 4,5,6,7 and 8 if no digit is repeated? 8. Given five flags of different colors, how many different signals can be made by hoisting them on a vertical staff if (a) three flags are used for each signal? (b) at least two flags must be used for each signal ? 9. How many numerals can be formed by using all the digits 2,4,5,7 and 9 with no digit being repeated? How many of these numbers are multiples of 5? How many of these are even? How many of these are greater than 70,000? How many of these are less than 50,000? 10. In how many ways can a 10 True/False examination question be answered? 11. A state report on crime consists of eight volumes numbered 1 to 8. In how many ways can these volumes be placed on a shelf?
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