Permutations using multiple vectors of different lengths

I am trying to sum values of all permutations of values from multiple matrices of different lengths, and cannot find a way to use perms or for loops to do it.

v1=[10,600,800];
v2=[6,13];
v3=[5,2];
v4=[10,15,22,6];
v5=[12,5];

I want each matrix to contribute one (and only one) value to the permutation. Ultimately, I'm looking for a list that shows something like the following:

10+6+5+10+12=43
10+6+5+10+5=36
10+6+5+15+12=45
...
800+13+2+6+5=826

Even better would be if I could figure out how to get it to show the indexes used for each one as follows:

(1)+(1)+(1)+(1)+(1)=43
(1)+(1)+(1)+(1)+(2)=36
(1)+(1)+(1)+(2)+(1)=45
...
(3)+(2)+(2)+(4)+(2)=826

Any help is greatly appreciated. Thank you.

[John D'Errico]

help ndgrid

Think about what it does.

[Robert Rieke]

ndgrid may work, but I'm having a difficult time understanding how it would be implemented.

Answer 1

[David Hill]

If the number of matrixes does not change (in this case 5 different maxtrixes,a b,c,d,e), for-loops could be used this way:

output=zeroes(1,length(a)*length(b)*length(c)*length(d)*length(e));
count=1;
for i1=a
    for i2=b
        for i3=c
            for i4=d
                for i5=e
                    output(count)=i1+i2+i3+i4+i5;
                    count=count+1;
                end
            end
        end
    end
end

[David Hill]

If you want indexes, this output produces each index used to obtain the sum.

function output = sumPermMatrixes(a,b,c,d,e)
output=zeros(length(a)*length(b)*length(c)*length(d)*length(e),6);
count=1;
for i1=1:length(a)
    for i2=1:length(b)
        for i3=1:length(c)
            for i4=1:length(d)
                for i5=1:length(e)
                    output(count,:)=[i1,i2,i3,i4,i5,a(i1)+b(i2)+c(i3)+d(i4)+e(i5)];
                    count=count+1;
                end
            end
        end
    end
end
end

[Robert Rieke]

Those answers worked well, thank you! The code in the first version should have "zeros" instead of "zeroes", but that's not a big deal.