Three dwarves and three elves sit down in in the row of six chairs. If no dwarf will sit next to another dwarf and no elf will sit next to another elf, in how many different ways can the elves and dwarves sit.My approach (2 mins 20 seconds):

We have 6 slots. The first slot could be filled with any of the 6 dwarves or elves (then 6 possibilities). The second, could only be filled with the other half of the group, depending if the first was filled with a dwarve or an elve (then 3 possibilities). The third, could only be filled with the 2 dwarves or the 2 elves remaining (then 2 possibilities). And the fourth could only be filled with the other 2 dwarves or elves (2 possibilities). The rest is filled with either one elve or one dwarve.

6*3*2*2= 72

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