Choosing 5 marbles out of 100 identical marbles? 
In how many ways can $5$ marbles be chosen out of $100$ identical marbles? 

Why does my book say there is only one way to make this selection?
 A: As you say in comments that the answer to your problem is $1$. I think it depends on the conception we have of the wording. Two possibilities:


*

*"Identical" is there to indicate the order in which you take the marbles is not important. In this case, it is like you asked to take $5$ people out of a group of $100$ people. Let $A_{i}$ be a person of this group ($i=1,\dots,100$). Then, taking $A_{1}$, $A_{8}$, $A_{84}$, $A_{52}$, $A_{31}$ is the same as taking $A_{84}$, $A_{8}$, $A_{31}$, $A_{52}$, $A_{1}$, which means the order doesn't matter. For the first person you choose, you have $100$ possibilities. For the second, you have $100-1=99$ and so on. So you have 
$$(100)\cdot(100-1)\cdot(100-2)\cdot(100-3)\cdot(100-4)$$
But you have counted the same group too many times: all the permutations of $5$ people, actually, which is $5!$. So the total number of possibilities is:
$$\frac{(100)\cdot(100-1)\cdot(100-2)\cdot(100-3)\cdot(100-4)}{5!}=\frac{100!}{5!(100-5)!}={100\choose 5}$$

*"Identical" means you can absolutely not make a difference between two marbles. Then, there is only one way to take $5$ marbles out of $100$ marbles because you won't be able to see the difference between two choices.
It is important to note that, in combinatorics, it is rarely the second case that applies (I say that because it is not a very interesting question, so that I often see "identical" to say "we can't see the difference in term of order"). We often consider that "identical" means the "order doesn't matter" and it is equivalent to name the marbles and to consider them as group of people. But I agree that, in order to avoid confusion, if we want the answer 1., the correct wording should be "In how many way, no matter the order, can we take $5$ marbles out of $100$ marbles?".
Your book is completely right, actually, since the wording has to be considered as completely identical.
A: Well, if each marble can be chosen once, we can choose 5 out of 100. So we have $$\frac{n*(n-1)*(n-2)*(n-3)*(n-4)}{5!}$$ choices where $n=100$. This can also be described as $$100\choose{5}$$ which is equivalent to 75287520.
A: Since the marbles are identical, it doesn't matter which set of $5$ marbles you take, it only matters how many marbles you take. And you are always taking $5$ marbles. Any set of 5 is indistinguishable from any other set of 5. So the answer is that there is $\boxed{1}$ way.
