This morning we enter class to Miss. Apple's problem of the day. The problem involves the students in the school and the use of the Venn Diagram

"A student survey was taken at Hive elementary on their favorite color, in 127 students, 74 students like red, 89 students like blue, 52 students like orange, 49 students like red and blue, 28 students like red and orange, 37 students like orange and blue, and 15 students like red, orange, and blue. How many students that like orange and do not like red took the survey? How many students who do not like red also do not like blue?"

After 15 minutes to work on the problem Miss. Apple takes up the question, after completing the Venn diagram, 24 students liked orange that don't like red, and 13 students do not like red as well as blue.

After class, it was time for class pictures, since the class was a 5/6 split with 6 grade five students and 23 grade six students. How many different ways can the class choose 4 students to move the benches if they cannot all be from the same grade?

The students and teacher wonder, as the photographer figures out that by picking 4 from the class of 29 with the exclusion of picking 4 students from the same grade, comes up with 14881 ways to choose 4 students to move the benches over to the photo area. 

After the students finished, the teachers of grades 7 and 8 lined up to take photos when a problem occurred, the 12 of them wanted to sit at a square table for a photo with 3 seats on each of the four sides, they thought how many different seating arrangements were possible?