A friend of mine is giving a dinner party. His current wine supply includes 9 bottles of zinfandel, 7 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries.
(a) If he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this?(b) If 6 bottles of wine are to be randomly selected from the 30 for serving, how many ways are there to do this?

a) 783 ways; b) 593775 ways

Step-by-step explanation:

a) Your friend wants to select 3 zinfandel out of 9 from the supply in a particular order, which means:

= 783

In the dinner party, the friend will have 783 ways of serving the zinfandel.

b) Now, your friend want to select 6 bottles out of 30 in no particular order and randomly selected. So:

= 593775

If you select 6 bottles randomly from 30, you will have 593775 ways of doing it.

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

describing distributions is one of the key skills you’ll need to earn a high score on the ap statistics exam. if you need proof of this, just flip through some past exam questions, which can be found at the collegeboard website. you’ll notice that the first free response question is almost always a question requiring you to look at a graph and describe it.

step-by-step explanation: just trying to get points sorry : (