Yes, but that doesn't give the output which he wants, which is the total number of pairs. For each string, you can use the formula n(n-1)/2 to get the number of pairs (4 copies of a string = 4(3)/2, or 6 pairs), or just add all the pairs as you go:

use strict;
use warnings;

my (%hash, $pairs);

while (<DATA>) {
    chomp; $pairs += $hash{$_}++;
}

print $pairs;

__DATA__
string1
string2
string3
string1
string1
string7
string2
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