2. In a big room, there are 4 hobbits: Frodo, Sam, Pippin and Merry, 3 elves: Galadriel, Elrond and Arwen, and 2 dwarfs:
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2. In a big room, there are 4 hobbits: Frodo, Sam, Pippin and Merry, 3 elves: Galadriel, Elrond and Arwen, and 2 dwarfs:
2. In a big room, there are 4 hobbits: Frodo, Sam, Pippin and Merry, 3 elves: Galadriel, Elrond and Arwen, and 2 dwarfs: Gimli and Thorin. (a) In how many ways can they stand in line, if all elves are standing next to each other? (b) In how many ways can you choose a committee of 5, if exactly 2 members are hobbits and there is at most 1 dwarf? (c) In how many ways can they stand in line, if none of Galadriel, Elrond, Arwen, Gimli and Thorin are standing next to each other?
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