Sum over multiple indices that take specific values

Question

Pretty simple question: how do I sum over multiple indices that can only take specific values all together?

To clarify: let's say I have the following sum:

$\sum p_{a,b,c} f(a,b,c)$

where $f$ is a function and $p$ is a coefficient (number) still in symbolic form, both dependent on indices $a,b,c$. Here {$a$, $b$, $c$} can take values specified by a list of three numbers, like {1,2,3}, {3,6,7} and so on. My idea is that I have a list of triplets, and I would like the sum to run on these triplets by assigning $a$ to the first number, $b$ to the second and $c$ to the third. So let's say that for a list of triplets

list={{1,2,3},{3,6,7},{2,6,9}}

The outcome should be

$p_{1,2,3}f[1,2,3]+p_{2,6,9}f[2,6,9]+p_{3,6,7}f[3,6,7]$

I was able to do it with Apply if there was only a function, but the coefficients $p$ need to carry the indices so it becomes tricky.

Answer 1

Here's one way:

Total[Subscript[p, #] & /@ lst f @@@ lst]

or

Total[Subscript[p, #] & /@ lst f /@ lst]

But you're probably making a mistake defining your p's this way, especially if you later need to do something with them. If you are willing to define p as a function, then

Total[p @@@ lst f @@@ lst]

would work.