combination

**shilz222** · January 27th 2008, 01:23 PM

$8$ bottles of zinfandel

$10$ bottles of merlot

$12$ bottles of cabaret.

(a) If he wants to serve $3$ bottles of zinfandel and serving order is important, how many ways are there to do this?

$\frac{8!}{5!} = 336$

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

$\binom{30}{6} = 593,775$

(c) If $6$ bottles are randomly chosen, how many ways are there two bottles of each variety being chosen?

(d) If $6$ bottles are randomly chosen, what is the probability that this results in two bottles of each variety being chosen.

(e) If $6$ bottles are randomly chosen, what is the probability that they are all the same variety?