How many different arrangements of three boxcars can be selected from eight boxcars for a train? The order is important since each boxcar is to be delivered to a different location.

(it's about permutation)

It's straightforward.

How many ways can 3 items be chosen from 8 when order matters?

P(8,3)=\frac{8!}{(8-3)!}

Thanks! :)

How many different signals using 3 distinct flags can be made if there 5 different flags from which to select?

It's the same type of problem. Apply what I done in the first post.

5C3=10 am I right?

is it a combination?

In how many ways can 6 individuals be seated in a round table with 6 chairs?

a) suppose 2 persons wanted to be seated side by side, in how many ways can they do it?

b) in how many ways can these 6 individuals arrange themselves if 2 among them refuse to sit together?

Follow up: is the problem a permutation or a combination? Thanks for the answer!

5C3=10 am i right?

If I understood well, no, that's not it. Order is still important.

Hence, the answer is 5P3, or 60

Otherwise, if order is not important, like for example Red Blue Yellow is the same as Blue Yellow Red, then it's combinations.