In how many different ways can 3 girls and 3 boys be seated at a rectangular table that has 3 chairs on one side and 3 stools on the other side, if two girls or two boys can never sit side by side?	Select the correct option
A) 24 B) 36 C) 72 D) 84 E) 96
The prompt gives us the specific restriction that a boy can't sit next to another boy and a girl can't sit next to another girl. Since there are chairs on one side of the table and stools on the other side of the table, we have to account for 2 possible seating arrangements:   BGB   GBG   and   GBG   BGB   From here, we can use a simple permutation to get to the answer:   Moving from left-to-right....   For the firstspot, there are 3 different boys to choose from   For the secondspot, there are 3 different girls to choose from   For the thirdspot, there then 2 different boys to choose from   For the fourthspot, there are then 2 different girls to choose form   For the fifth and sixthspots, we have the 1 boy and 1 girl that are left   (3)(3)(2)(2)(1)(1) = 36 possible seating arrangements for each of the two options.   (36)(2) = 72   72
<result>C</result>
In how many different ways can 3 girls and 3 boys be seated at a rectangular table that has 3 chairs on one side and 3 stools on the other side, if two girls or two boys can never sit side by side?