This paper presents the first evidence of how students make career technical education (CTE) course-taking decisions. Among the universe of Michigan high-schoolers we find large disparities in CTE access and participation by gender, race, and income. We decompose participation gaps between supply (access) and demand (preferences) with a simple discrete choice model. We find that student preferences for CTE content drive participation gaps by gender, inequities in access drive gaps by income, and school-level supply and demand factors combine to create the gaps by race. Policy simulations highlight the importance of accessible CTE delivery models within comprehensive high schools.