CHAPTER 9 / SPECIAL MATH PROBLEMS 351
- What is the fundamental counting principle?
- How many different four-letter arrangements of the letters LMNO can be made if no letter can be repeated?
Answer this first by listing all of the possible arrangements, then by using the Fundamental Counting Prin-
ciple, and check that the two answers agree. - If the first digit of a 3-digit area code cannot be 0 and the second digit is either 0 or 1, then how many dif-
ferent area codes are possible? - A baseball team has six players, each of whom can play in any of the three outfield positions: left field, cen-
ter field, and right field. How many possible different arrangements of these players can the team place in
the outfield? (This one is a bit harder to do by listing!) - Among a set of 40 sophomores, 20 students take French and 27 students take Spanish. If all of the students
take either French or Spanish, how many students take both French andSpanish? - A box contains buttons, each of which is either blue or green and has either two or four holes. If there are
four times as many blue buttons as green buttons and six times as many four-holed buttons as two-holed
buttons, what is the leastnumber of buttons that could be in the box?
Concept Review 5: Counting Problems