{"status": "success", "data": {"description_md": "Two counterfeit coins of equal weight are mixed with $8$ identical genuine coins. The weight of each of the counterfeit coins is different from the weight of each of the genuine coins. A pair of coins is selected at random without replacement from the $10$ coins. A second pair is selected at random without replacement from the remaining $8$ coins. The combined weight of the first pair is equal to the combined weight of the second pair. What is the probability that all $4$ selected coins are genuine?\n\n$\\textbf{(A)}\\ \\frac{7}{11}\\qquad\\textbf{(B)}\\ \\frac{9}{13}\\qquad\\textbf{(C)}\\ \\frac{11}{15}\\qquad\\textbf{(D)}\\ \\frac{15}{19}\\qquad\\textbf{(E)}\\ \\frac{15}{16}$", "description_html": "<p>Two counterfeit coins of equal weight are mixed with <span class=\"katex--inline\">8</span> identical genuine coins. The weight of each of the counterfeit coins is different from the weight of each of the genuine coins. A pair of coins is selected at random without replacement from the <span class=\"katex--inline\">10</span> coins. A second pair is selected at random without replacement from the remaining <span class=\"katex--inline\">8</span> coins. The combined weight of the first pair is equal to the combined weight of the second pair. What is the probability that all <span class=\"katex--inline\">4</span> selected coins are genuine?</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}\\ \\frac{7}{11}\\qquad\\textbf{(B)}\\ \\frac{9}{13}\\qquad\\textbf{(C)}\\ \\frac{11}{15}\\qquad\\textbf{(D)}\\ \\frac{15}{19}\\qquad\\textbf{(E)}\\ \\frac{15}{16}</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2011 AMC 10A Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/11_amc10A_p22", "prev": "/problem/11_amc10A_p20"}}