How would we do this using COMBINATIONS/C as opposed to permutations or just counting out possibilities for each of the 6 slots (ie 6x3x2x2)?
You need to arrange the 6 people in 6 places. You can think in terms of combinations in the following way:
For the first chair, we select any one person of the 6 in 6C1 ways.
For the second chair, we select any one from the 3 in 3C1 ways (e.g. if an elf is sitting on the first chair, we need to choose out of the 3 dwarves only)
For the third chair, we select one of the leftover 2 (e.g. one elf is already sitting in first chair) in 2C1 ways
For the fourth chair, we select one of the leftover 2 (e.g. one dwarf is already sitting in the second chair and we need to choose of the remaining 2) in 2C1 ways
For the fifth and sixth chairs, there is only one choice each.
Answer: 6C1 * 3C1 * 2C1 * 2C1 = 6*3*2*2 = 72
(note that this is the basic counting principle itself. For more, check: http://www.veritasprep.com/blog/2011/10 ... inatorics/
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