# How many ways are there to invite different subsets of 3 out of 5 friends on 3 successive days?

My question is:

How many ways are there for a woman to invite different subsets of three of her five friends on three successive days? How many ways if she has n friends?

I know there are C(5,3) ways to select a different subset of 3 friends out of 5, but how would you ensure that the subsets were all different on three consecutive days?

Also, for the second part, would you not just replace any "5" in the answer to the first part with n to get a general formula?

Thanks all.

As you mentioned that there are $$C(5,3)=10$$ ways to choose subset of 3 friends out of 5. Now you need to fill 3 places(three consecutive days) using 10 distinct subset of friends which is $$\begin{equation} P(10,3) = 720 \end{equation}$$
On the first day, she can invinite any 3 friends, so she has $${5}\choose {3}$$ options. On the second day, she must not choose the same subset as on the first, and on the second day she must not invinite one of the two sets from the day before. Therefore she has $${{5}\choose {3}} \cdot ({{5}\choose {3}}-1) \cdot ({{5}\choose {3}}-2)=720$$ options.