"independent trials" notation in Ross' book In the book "Introduction to Probability Models", while explaining "independent trials", author Ross uses some numerical subscripts that I can not understand. I am quoting the paragraph, can you explain?

Suppose that a sequence of experiments, each of which results in either a "success" or a "failure," is to be performed. Let $E_i$, $i \geq 1$, denote the event that the $i$th experiment results in a success. If, for all $i_1,i_2,\ldots,i_n$ $$P(E_{i_1}E_{i_2} \cdots E_{i_n}) = \prod^n_{j=1} P(E_{i_j})$$

In other words, let $i$ be $2$. $E_2$ is the event second experiment results in a success. What is $2_1$, and what is $E_{2_1}$?
Thanks a lot.
 A: The $i$ and the $i_j$ are just dummy variables and have no relations to each other. In less ambiguous but more pedantic language, suppose we have events $E_1, E_2, \dots$. (I'm not sure if the author intends to have only finitely many events here, but it doesn't matter.) For any distinct indices $i_1, \dots, i_n$, we have
\begin{align*}
P(E_{i_1} \cdots E_{i_n}) = P(E_{i_1}) \cdots P(E_{i_n})
\end{align*}
In the other words, the author is saying that any finite subset of the $E_1, E_2, \dots$ is independent. 
A: This is really about notation, not about probability or independence.
Notice that it says for all.  Thus: "For all $i_1,\ldots,i_n$".
As a concrete example, one could have $n=6$ and
$$
i_1 = 23, \quad i_2 = 10, \quad i_3=5, \quad i_4=971, \quad i_5 = 154, \quad i_6=3.
$$
Then one would be asserting that
$$
P(E_{23} \, E_{10} \, E_{5} \, E_{971} \, E_{154} \, E_3) = P(E_{23})\,P(E_{10})\,P(E_5)\, P(E_{971}) \, P(E_{154}) \, P(E_3).
$$
The words for all mean that if you had picked any other sequence of values of the indices, or any other number besides $6$, the corresponding thing would still be true.
