adding n-tuples

[kwatts59]

There are two arrays, each with n numbers. How do I calculate the sum of all the possible n-tuples.

For example, array @A has 4 numbers and array @B has 4 numbers as follows:

@A = ($a1,$a2,$a3,$a4);
@B = ($b1,$b2,$b3,$b4);

How do I calculate the sum of all 4-tuples?

$E = b1*a2*a3*a4 + a1*b2*a3*a4 + a1*a2*b3*a4 + a1*a2*a3*b4 +
b1*b2*a3*a4 + b1*a2*b3*a4 + b1*a2*a3*b4 +
a1*b2*b3*a4 + a1*b2*a3*b4 + a1*a2*b3*b4 +
b1*b2*b3*a4 + b1*b2*a3*b4 + b1*a2*b3*b4 + a1*b2*b3*b4 + b1*b2*b3*b4;

Note that there are no duplicate numbers or positions. Ex. a1*a1*a2*a2 or a1*b1*a2*b2 are not counted.

Edit: I forgot the last 4-tuple b1*b2*b3*b4

2019-05-17 Athanasius added code tags