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The board of directors for a particular company consists of 10 members, 6 of whom are loyal to the current company president and 4 of

The board of directors for a particular company consists of 10 members, 6 of whom are loyal to the current company president and 4 of whom want to fire the president. Suppose the chair of the board (who is a loyal supporter of the current president) suggests to randomly select 4 other board members to serve on a committee to decide the president's fate. Find the probability for the first 3 questions and explain your answer for the fourth question.

What is the probability that all 5 committee members will vote to keep the president in place, if no one changes their minds?

What is the probability that a majority of the committee will vote to keep the president in place, if no one changes their minds?

What is the probability that the vote is 4 to 1 to replace the president, if no one changes their minds?

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