There are 6 candidates running in a Presidential primary. After each primary, two of the candidates will withdraw, except for the last one, when the winner becomes the nominee. (a) The first primary has all 6 candidates. In how many ways could the 6 candidates finish the race? (b) The second primary will only have the top 4 finishers from the first race. How many ways could the 4 candidates finish the second race? (c) The third primary only has the 2 remaining candidates. How many ways could this race finish?

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A:

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A:

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A: see my solution below

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.