Part 2:

#
# Combination
#
#                 n!
#    C(n, r) = --------
#              r!(n-r)!
#

sub C {
   my ($n, $r) = @_;
   my $c = 1;
   $c *= $n--/$r-- for 1..$r;
   return $c;
}

sub calcIt {
   my ($n, $d) = @_;
   return C($n+$d+2-1, $d+2);
}

print(calcIt(10, 5), "\n");  # 11440
print(calcIt(20, 5), "\n");  # 657800
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