{"status": "success", "data": {"description_md": "A choir director must select a group of singers from among his $6$ tenors and $8$ basses. The only requirements are that the difference between the numbers of tenors and basses must be a multiple of $4$, and the group must have at least one singer. Let $N$ be the number of different groups that could be selected. What is the remainder when $N$ is divided by $100$?\n\n$\\textbf{(A) } 47\\qquad\\textbf{(B) } 48\\qquad\\textbf{(C) } 83\\qquad\\textbf{(D) } 95\\qquad\\textbf{(E) } 96\\qquad$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>A choir director must select a group of singers from among his <span class=\"katex--inline\">6</span> tenors and <span class=\"katex--inline\">8</span> basses. The only requirements are that the difference between the numbers of tenors and basses must be a multiple of <span class=\"katex--inline\">4</span>, and the group must have at least one singer. Let <span class=\"katex--inline\">N</span> be the number of different groups that could be selected. What is the remainder when <span class=\"katex--inline\">N</span> is divided by <span class=\"katex--inline\">100</span>?</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A) } 47\\qquad\\textbf{(B) } 48\\qquad\\textbf{(C) } 83\\qquad\\textbf{(D) } 95\\qquad\\textbf{(E) } 96\\qquad</span></p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2021 AMC 12A Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/21_amc12A_p16", "prev": "/problem/21_amc12A_p14"}}