In the U.S., engineering and computing programs usually follow a 128-credit bachelor's degree requirement followed by a 30-credit master's degree program. A combined bachelor's and master's degree, commonly known as the 4+1, is designed to reduce the conventional time by educating students on engineering fundamentals as well as advanced discipline-specific knowledge content. With the increased competitiveness and demands of the workforce, such combined programs provide minority students with a competitive edge. However, fewer students take advantage of such combined programs. Therefore, this research aims to identify the reasons behind the low interest in applying and enrolling in the 4+1 programs. This research utilizes a mixed research method approach to understand and assess student's knowledge, level of understanding, and perception of the 4+1 programs through the administration of a survey to 486 undergraduate students at the College of Engineering and Computing in a minority-serving institution, Florida International University. A binary logistic regression model was then developed to determine the variables influencing the expected student enrollment in the combined programs. From the obtained results of the undergraduate graduating student survey, 25% of the students indicated their intention to apply for graduate studies post their undergraduate and 58% maintained a GPA above 3.0, which reflects their readiness and possible eligibility to apply for a 4+1 program prior to their graduation. The findings of the study provide a deeper understanding of students' motivational factors for joining 4+1 programs, current effective and ineffective recruiting practices, and the various opportunities offered by such programs. As poor and lack of diversity continues to be an issue in engineering especially in graduate programs, 4+1 programs foster an immense potential to attract and increase the number of underrepresented students in graduate education as well as retain and recruit top candidates for the doctoral programs.