Thanks for making me think about regex in yet another way!! Here is a easy to understand code
use strict;
use warnings;
my $str="";
for $str('aaa'..'ccc')
{
    
    if($str=~m/^[abc]{3}$/)
    {
        if($str!~m/(.*a.*a)/)
        {
            if($str!~m/(.*b.*b)/)
            {
                if($str!~m/(.*c.*c)/)
                {
                    print "\' $str \' is a Match\n";
                }
                else
                {
                    print "The string $str contains duplicated 'c'\n";
                }
            }
            else
            {
                print "The string $str contains duplicated 'b'\n";
            }
        }
        else
        {
            print "The string $str contains duplicated 'a'\n";
        }
    }
    else
    {
        print "Either the string \'$str\' contains a character not bel
+onging to the class [abc] or is more than 3 characters\n";
    }
}

[download]
which can be condensed as 
use strict;
use warnings;
my $str="";
for $str('aaa'..'ccc')
{
    if($str=~m/^[abc]{3}$/ && $str!~m/(.*a.*a)/ && $str !~ m/(.*b.*b)/
+ && $str!~ m/(.*c.*c)/)
    {
        print "\' $str \' is a Match\n";
    }
    
}

[download]
UPDATE: I overlooked the complexity of the problem.Thanks to Punitha,merlyn,KurtSchwind for their inputs

The world is so big for any individual to conquer

In reply to Re: REgular expression to check the string that allows "a","b" and "c" to occur only once in any order. by narainhere
in thread REgular expression to check the string that allows "a","b" and "c" to occur only once in any order. by isha

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