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Writing 'rights' right!

The principle of the social services is that people have rights to live happily and without discrimination.

I know, I know. You mention more than one right. Normally your teacher would be yelling at you to add an 's'. But this is a vocabulary/collocation issue.

The principle of the social services is that people have the right to live happily and without discrimination.

You can think of it as a phrasal verb (Indonesians will be translating berhak untuk..). Sometimes it's have the right to + V1, and sometimes have a right to + V1.
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To see relative frequencies we can consult Google NGRAM viewer:

NGRAM Rights