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.

360 cm

Step-by-step explanation:

Here, one cylinder is right and the other cylinder is oblique or slanted.

In geometrical context, an object which is distorted so that it seems to lean over at a certain angle, in comparison to being completely upright is called an oblique object. While the right objects are exactly upright.

Since both the cylinders have the same base and height, so their volume is not affected by the lean of the cylinder B.

Therefore, cylinder B has the same volume as cylinder A i.e. 360 cm.