Three dwarves and three elves sit down in a row of six chairs. If no dwarf will sit next to another dwarf and no elf wil sit next to another elf, in how many different ways can the elves and dwarves sit?	Pick one.
A) 16 B) 26 C) 36 D) 63 E) 72
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= 
<gadget id="calculator">6*3*2*2</gadget>
<output>72</output>
72   ANS:72
<result>E</result>
Three dwarves and three elves sit down in a row of six chairs. If no dwarf will sit next to another dwarf and no elf wil sit next to another elf, in how many different ways can the elves and dwarves sit?