Hi Awli,
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 first "spot", there are 3 different boys to choose from
For the second "spot", there are 3 different girls to choose from
For the third "spot", there then 2 different boys to choose from
For the fourth "spot", there are then 2 different girls to choose form
For the fifth and sixth "spots", 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
Final Answer:
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