Assuming you have some way of identifying the correct answer implies you have access to that data. Therefore you could use List::Util::shuffle once you have all elements in a single list. Something like:

use List::Util qw(shuffle);
use Data::Random::WordList;

my $correct = "Correct answer";
my $wl = new Data::Random::WordList( wordlist => '/usr/dict/words' );
my @rand_words = $wl->get_words(3);
my @answers = shuffle(@rand_words, $correct);
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A. pick 1 random question from the Questions text file

Read the questions from the question file into an array, and randomly pick one of the array elements using rand.

B. ALWAYS pick the right answer and 3 random wrong answers from the Answers text file

Using the question number from the last step, go get the correct answer from the answer file, possibly again reading the answers file into an array.

For the wrong answers, make some stuff up and put it in a bad answers file. Read that file into an array as before, and randomly select three distinct answers (distinct, because you don't want the same wrong answer twice). Order these three answers and the correct answer randomly and display. Done!