Using the Set::CrossProduct module, here is another approach to your present solution. 
#!/usr/bin/perl
use strict;
use warnings;
use Set::CrossProduct;
use List::Util 'sum';

my $targetSum = 4;
my @freq = qw (0.1 0.2 0.7);
my $nElements = 2;
my @combo = ([0..$#freq]) x $nElements;

my $cross = Set::CrossProduct->new( \@combo );

my @ways;
while( my $array_ref = $cross->get ) {
    push @ways, $array_ref if sum(@$array_ref) == $targetSum;
}

#Now calculate P-value
my $pVal;
for my $aref (@ways) {
    my $p = 1;
    for my $operand (@$aref) {
        $p *= $freq[$operand];
        }
    $pVal += $p;
    }
print "P-value(sum of $nElements = $targetSum) = $pVal\n";

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In reply to Re: Probability sum of random variables by Cristoforo
in thread Probability sum of random variables by FFRANK

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