I have 30 photos to post on my website Im planning to post t

I have 30 photos to post on my website. I\'m planning to post these on two web pages, one marked \"Friends\" and the other marked \"Family\". No photo may go on both pages but every pohoto will end up on one or the other. Conceivably, one of the pages may be empty.
Please answer these two questions:
a. In how many ways can I post these photos to the web pages if the order in which the photos appear on those pages matter?
b. In how many ways can I post these photos to the web pages if the order in which the photos appear on those pages does not matter?

Solution

A)

This is like a balls and urns problem. That is, if there are n distinct balls to be distributed in r urns, there are (n + r - 1)! ways to do it.

Here, n = 30, r = 2. Thus, there are (30+2-1)! = 31! ways or approx 8.22284*10^33. [answer]

b)

If the order does not matter, note that each photo has two ways to choose. Thus, there are 2^30 = 1073741824 ways to do it. [answer]