Discrete Math Combination Problems... Math Geniuses: Please help?

[breeze887]

1. I plan to form a committee of 5 members. chosen from are 6 physicists, 2 chemists, 1 mathematician. In how many ways can this be done so as to include:
a) 1 mathematician
b) 4 physicists
c) not more than 4 physicists

2. Combination for 6/42 lotto
3. In how many ways can the letters of the word COMBINATION be arranged if the two (I's) can be separated?
4. Four (4) are to be selected from the seven (7) letters of the word STUDENT.
5. Find the number of different 4 letter selection than can be made with:
a) no T
b) one T
c) two T's

Thank you so much in advance and God bless! ^^,