Permutation

1) Lay out 13 cards (Ace to King) in a row in some random order.  2) Move the Ace to the front of the row, such that it leaves an empty space. (7A9... becomes A7_9...).  3) Swap the empty space with t...

1. A schoolhas 11 teachers: 6 Math/Science teachers, 4 Humanities teachers, and 1 Phys-edteacher. They are arranging themselves in a row for a year-end photo.a. Determine how many ways the teachers ca...

A dog owner wants to buy their dog 3 things at a specialty pet shop. The shop has 3 different types of dog treats, 4 different types of toys and 5 different pieces of clothing. What is the probability...

I'm trying to calculate total possible unique potential combinations.  I'm trying to solve for a tv dinner tray with 4 little sections for one each of:  meat, veggie, starch, dessert.  These sections...

Permutation and follow on questions. Please see attachment.

Homomorphism

Please see questions on attachment 

I am confused about counting all possible ways that $n$ persons can seat around a round table.