A friend of mine is giving a dinner party

A friend of mine is giving a dinner party. His current winesupply includes 8 bottles of zinfandel, 10 of merlot and 12 ofcabernet (he only drinks red wine), all from different wineries.

a.) if he wants to serve 3 bottles of zinfandel and servingorder is important, how many ways are there to do this?

b.) If 6 bottles of wine are to be randomly selected from the 30for serving, how many ways are there to do this?

c.) IF 6 bottles are randomly selected, how many ways are thereto obtain two bottles of each variety?

d.) IF 6 bottles are randomly selected, what is the probabilitythat this results in two bottles of each variety being chosen?

e.) If 6 bottles are randomly selected, what is the probabilitythat all of them are the same variety?