combinatorics

a dinner party is arranged for 16 people. the people will be seated along 2 sides of a rectangular table with 8 chairs on each side. 4 people wish to sit on one particular side and a couple wishes to sit together on the other side. how many ways can 16 people be arranged!!!!! how do i get the...

If a committee of 6 members is chosen from 4 teachers and 6 students, what is the probability that it contains 2 teachers and 4 students. Can someone please explain to me why we have to divide the answer by 10C6??

I just started learning this topic so please don't laugh at me if you find this question easy but I can't do any of these ..... Can you guys please help me out with this entire question??

I stumbled upon this question from the MANSW textbook. It is part g) and h) that are troubling me What does three of a kind mean? And how do I do those parts?