The 20 colleges of interest to a high school senior include 8 that are expensive ( tuition more than 20,000 per year), 8 that are far from home( more than 200 miles away), and 7 that are both expensive and far from home. If the student decides to select a college that is not expensive and within 200 miles from home, how many selections are possible?

Answer: 6Step-by-step explanation:Let  S= Total collegesA = colleges are expensive.B= colleges are  far from home( more than 200 miles away).Given : n(S)= 20n(A)=8n(B)=8n(A∩B) =2Then, the number of  college that are not expensive and within 200 miles from home :-[tex]n(A'\cap B')=n(S)-n(A\cup B)\\\\=20-(n(A)+n(B)-N(A\cap B))\ \ [\because\ n(A\cup B)=n(A)+n(B)-N(A\cap B)]\\\\=20-(8+8-2)\\\\=20-14=6[/tex]i.e.  the number of  college that are not expensive and within 200 miles from home=6Hence, the number of possible selections are 6 .