Supervised machine learning is widely used for selection problems where an individual is selected among a pool of applicants. This problem can be applied in loan lending, hiring, and university admission. Machine learning models often suffer from a bias towards specific sensitive attributes (e.g., race, gender) as a reflection of pre-existing discrimination in the dataset. On top of unfairness, privacy concerns may incur when models are trained on sensitive personal information. In this work, we study the possibility of using a differentially private Laplace mechanism to enhance fairness and privacy in the selection problem. Also, we defined a condition that can make the selection problem fair and private.