At the time of this writing, Wikipedia lists 12 Republican presidential candidat

Question

At the time of this writing, Wikipedia lists 12 Republican presidential candidates as being listed in major polls, which presumably means they are viable candidates. (Five candidates who were in major polls have already dropped out.) When networks try to limit the number of candidates on stage for debates, there are many possible outcomes.

1) How many ways are there to pick six candidates out of the 12 to be in a debate? Here, we are only concerned about which candidates are chosen.

2) Once the six candidates are chosen, how many different ways are there to seat them in six chairs across the stage? Assume only one candidate sits in each chair, and assume the chairs are big enough to hold them.

3) Once the six candidates are chosen, how many different ways are there to seat them in six chairs in a circle on a circular stage? Here, rotating a configuration does not make it a new configuration

4) If you were an engineering student who had no knowledge of politics, what is the probability that you could correctly guess the order that the five dropout candidates dropped out?

5) If the Republican candidates for president and vice-president are chosen from the 12 current candidates, how many possible scenarios are possible for the top of the party ticket? Here, which of the two candidates is the presidential candidate does matter.

Explanation / Answer

1) 12C6 = 924

2) 12C6 * 6C1 = 5544

3)12C6 / 6 = 154

4)

Probability = 5 / 6

5)

10C4 = 210

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