Probability . Full answer please A multiple-choice test consists of 15 questions

Question

Probability . Full answer please

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? In an election there are three candidates for mayor, four candidates for city treasurer, five candidates for city manager, and three candidates for city attomey. In how many ways can a voter mark his ballot for all four of these offices? 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? How many distinct permutations are there of the letters in the word, "MISSISSIPPI"? Among the eight nominees for three vacancies on a city council are three men and five women. In how may ways can these vacancies be filled with one of the men and two of the women? How many different 5-card poker hands are possible containing four of a kind?

Explanation / Answer

1.

there are 15 questions and each question has 3 choices,

first question she can answer it in 3 ways (since 3 choices), sencond question she can answer it in 3 ways,...15th question she can asnwer it in 3 ways

3*3*3*3*3*3*3*3*3*3*3*3*3*3*3 = 315 = 14348907 different ways student can check off her answers to these questions.

2.

there are 3 candidates for mayor, 4 for city treasurer, 5 for city manager and 3 for city attorney

so mayor can be selected in 3 ways, city treasurer in 4 ways, city manager in 5 way and city attorney in 3 ways

i.e. 3*4*5*3 = 180 ways voter can mark his ballot for these four offices.

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