combinatorics

Using the letters P,P,Q,R,S,T,T, how many codes can be formed if they contain exactly four of the seven letters? i understand how to do this question if the codes contain all seven letters, but how would i approach this if they only contain four? the answer in the book is 5P4 + 2 x 4C2 x 4!/2...

this question is part of a 'using counting in probability' part of my textbook and i'm stuck on part (d). i tried working it out, but my answers are different from the textbook's (which is 1/425). any help would be appreciated <3

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?