Here are some hints:

For 2.15 (8 "+" signs and 6 "-" signs arranged with 5 sign changes):

Let's look at an example first: $\large{+--++++-+++---}$. Why does this have 5 sign changes? Well we have a plus, then some minuses (1st sign change), then some pluses (a 2nd sign change), etc. In other words, this example looks like $\large{(+)(-)(+)(-)(+)(-)}$, where, for example, (+) denotes some pluses. How many different ways could we arrange the +'s and -'s to get this? Are there other cases we need to consider?

For 2.16:

First off, try to answer this question first with some specific values of m, n, and k. For example, consider first something like m=6, n=5, and k=3. Then think about an idea similar to 2.15, where (G) denotes some green books and (B) some blue books. Once you do a few specific values hopefully the full pattern emerges!

Hope this helps! Let us know if you have any other questions.