Retrieve all possible combinations of n items of a given size k and apply the function sum to another column

I have a df that looks like:

  item value
1    a     1
2    b     4
3    c     3
4    d     2
5    e     6
6    f     8
7    g    11

df <- data.frame(stringsAsFactors=FALSE,
        item = c("a", "b", "c", "d", "e", "f", "g"),
       value = c(1L, 4L, 3L, 2L, 6L, 8L, 11L))

I want to generate all possible combinations of size = 3, for example:

size <- 3

combo_3 <- combn(df$item, size, simplify = F)

Now I want to summarize this result.

I want a dataframe with the following contents:

• Portfolio Index
• Items in the portfolio
• the sum of the column values ​​for that particular combination

Here is an example data frame where the first combination appears:

combo_index    item    sum_total
1                 a        8
1                 b        8
1                 c        8
2                 a        7
2                 b        7
2                 d        7
3                 a        11
3                 b        11
3                 e        11 
             ...
             ...
             ...