How many students are enrolled in a course either in calculus, discrete mathmati

Question

How many students are enrolled in a course either in calculus, discrete mathmatics, data structures, or programming languages at a school if there are 507, 292, 312, and 344 students in these courses respectively; 14 in both calculus and data structures, 213 in both calculus and programming languages; 211 in both discrete mathmatics, and data structures; 43 in both discrete mathmatics and programming languages; and no student may take calculus and discrete mathmatics, or data structures and programming languages concurrently?

Explanation / Answer

calculus (c), discrete mathmatics (m), data structures (s), or programming (p) c=507, m=292, s=312, and p=344 14 in both C+S, 213 in both C+P 211 in both M+S; 43 in both M+P; no student may take C+M, or S+P CMS - not permitted cm is not allowed CMP - not permitted cm CSP - not permitted sp MSP - not permitted sp TO solve, add c=507, m=292, s=312, and p=344 = 1455 if no one takes two courses, but... then subtract for students counted double 14+ 213+211+ 43 = 481 students were counted twice 1455-481=974

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