1. Seven candidates for mayor, four candidates for city council president, and six propositions are being put before the electorate. How many different ballots could be cast, assuming that every voter votes on each of the items? If voters can choose to leave any item blank, how many different ballots are possible?
2. Allison is preparing her applications for college. She will apply to three community colleges and has to fill out six parts in each of those applications. She will apply to three four-year schools, each of which has a seven-part application. How many application segments must she complete?
3. Consider the triangular display of letters below. Start with the letter T at the top and move down the triangle to a letter S at the bottom. From any given letter, move only to one of the letters directly below it on the left or right. How many different paths spell TEXAS?

4. A railway has 20 stations. If the names of the point of departure and the destination are printed on each ticket, how many different kinds of single tickets must be printed? How many different kinds of tickets are needed if each ticket may be used in either direction between two stations?

Transcribed Image Text:

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