Just for fun, a simulation to confirm:

use List::Util qw/shuffle sum/;
my $RUNS = 1_000_000;
my %counts;
for (1..$RUNS) {
    my @deck = shuffle 0..51;
    my $in_correct_loc = grep {$_==$deck[$_]} 0..51;
    $counts{$in_correct_loc}++;
}
print "Number of cards in the correct position: % of runs\n";
printf "% 4d: %.4f%%\n", $_, 100*$counts{$_}/$RUNS
    for sort {$a<=>$b} keys %counts;
my $one_or_more = sum map {$_//0} @counts{1..52};
printf "1-52: %.4f%%\n", 100*$one_or_more/$RUNS;

__END__

Number of cards in the correct position: % of runs
   0: 36.8130%
   1: 36.8086%
   2: 18.3846%
   3: 6.1085%
   4: 1.5349%
   5: 0.2926%
   6: 0.0487%
   7: 0.0080%
   8: 0.0010%
   9: 0.0001%
1-52: 63.1870%
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