1. A multiple-choice test consists of 15 questions, each permitting a choice of
ID: 3255068 • Letter: 1
Question
1. A multiple-choice test consists of 15 questions, each permitting a choice of three alternatives. In how many different ways can a student check off her answers to these questions?
2. In an election there are three candidates for mayor, four candidates for city treasurer, five candidates for city manager, and three candidates for city attorney. In how many ways can a voter mark his ballot for all four of these offices?
3. In how many ways can six people line up to get on a bus? In how many ways can they line up if two of the people refuse to follow each other?
Explanation / Answer
sOLUTION1:
3^15=14348907 WAYS
SOLUTION2:
=3C1*4C1*5C1*3C1=180 WAYS
SOLUTION3:
In 6! ways can six people line up to get on a bus=6!=720 ways
how many ways can they line up if two of the people refuse to follow each other?
6!-5*2*4!=480 ways
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