Help with combinations The sum of all the different ways to multiply together $a,b,c,d,\ldots$ is equal to $$(a+1)(b+1)(c+1)(d+1)\cdots$$ right?
If this is true? why is it true?

Yes it  is true, give it a try...
Ok, sorry. Here's a little more detail:

We have the identity
  $$
    \prod_{j=1}^n ( \lambda-X_j)=\lambda^n-e_1(X_1,\ldots,X_n)\lambda^{n-1}+e_2(X_1,\ldots,X_n)\lambda^{n-2}-\cdots+(-1)^n e_n(X_1,\ldots,X_n). 
$$
  $\biggr[$use $\lambda=-1$ to get $ \prod_{j=1}^n ( -1-X_j)=(-1)^n\prod_{j=1}^n ( 1+X_j)$$\biggr]$
This can be proven by a double mathematical induction with respect to the number of variables n and, for fixed n, with respect to the degree of the homogeneous polynomial.

I really thought that giving it a try would show some inside. 
Hope the links help,
