Cook the pasta according to the package directions. Drain and run under cold water.
Place the pasta, eggs, peppers, onion, celery, and carrots in a large bowl and toss to combine. Set aside.
In a medium bowl combine the mayonnaise, relish, mustard, vinegar, sugar, celery seed, salt, and pepper. Mix well to combine.
Pour the dressing over top of the pasta mixture. Mix well to combine.
Refrigerate for at least 4 hours before serving.