{"status": "success", "data": {"description_md": "Ms. Carr asks her students to read any $5$ of the $10$ books on a reading list. Harold randomly selects $5$ books from this list, and Betty does the same. What is the probability that there are exactly $2$ books that they both select?\n\n$\\textbf{(A)}\\ \\frac{1}{8} \\qquad\\textbf{(B)}\\ \\frac{5}{36} \\qquad\\textbf{(C)}\\ \\frac{14}{45} \\qquad\\textbf{(D)}\\ \\frac{25}{63} \\qquad\\textbf{(E)}\\ \\frac{1}{2}$", "description_html": "<p>Ms. Carr asks her students to read any  <span class=\"katex--inline\">5</span>  of the  <span class=\"katex--inline\">10</span>  books on a reading list. Harold randomly selects  <span class=\"katex--inline\">5</span>  books from this list, and Betty does the same. What is the probability that there are exactly  <span class=\"katex--inline\">2</span>  books that they both select?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac{1}{8} \\qquad\\textbf{(B)}\\ \\frac{5}{36} \\qquad\\textbf{(C)}\\ \\frac{14}{45} \\qquad\\textbf{(D)}\\ \\frac{25}{63} \\qquad\\textbf{(E)}\\ \\frac{1}{2}</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2020 AMC 10B Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc10B_p12", "prev": "/problem/20_amc10B_p10"}}