I’m a high school teacher and I’m doubting myself with this one.
I have nine groups of tables in my classroom and 34 students total. There is currently one group of five, six groups of four, A group of three and a group of two. I want the students to rearrange themselves so that they are all at a different table and they are sitting with all new students. How many possible combinations of student arrangements are there?
My thinking goes like this: The group of 5 has 8x7x6x5x4=6720 possibilities, six groups of four have 6x8x7x6x5=10080 possibilities, the groups of three and two have 8x7x6=336 and 8×7=56 possibilities, respectively. So we’re looking at a total of 17192 possible seating combinations.
Am I on the right track here? I feel like I’m missing something but I’m not sure what it is.