Selection for higher education (HE) programs may hinder equal opportunities for applicants and thereby reduce student diversity and representativeness. However, variables which could play a role in inequality of opportunity are often studied separately from each other. Therefore, this retrospective cohort study conducts an innovative intersectional analysis of the inequality of opportunity in admissions to selective HE programs. Using a combination of multivariable logistic regression analyses and descriptive statistics, we aimed to investigate 1) the representativeness of student populations of selective HE programs, as compared to both the applicant pool and the demographics of the age cohort; 2) the demographic background variables which are associated with an applicant's odds of admission; and 3) the intersectional acceptance rates of applicants with all, some or none of the background characteristics positively associated with odds of admission. The study focused on all selective HE programs (n = 96) in The Netherlands in 2019 and 2020, using Studielink applicant data (N = 85,839) and Statistics Netherlands microdata of ten background characteristics. The results show that student diversity in selective HE programs is limited, partly due to the widespread inequality of opportunity in the selection procedures, and partly due to self-selection. Out of all ten variables, migration background was most often (negatively) associated with the odds of receiving an offer of admission. The intersectional analyses provide detailed insight into how (dis)advantage has different effects for different groups. We therefore recommend the implementation of equitable admissions procedures which take intersectionality into account.