Canonical URI: https://w3id.org/kmath/textbook_solution/donga_solution_p157_p117_03
| rdf:type | math:TextbookSolution |
|---|---|
| rdfs:label | 동아 p117 문제 3 풀이 |
| rdfs:comment | 동아 공통수학1 정답 및 풀이 p157의 p117 문제 3번 풀이. |
| math:answerText | \({}_nC_r={}_{n-1}C_{r-1}+{}_{n-1}C_r\) |
| math:explanationText | \[ \begin{aligned} {}_{n-1}C_{r-1}+{}_{n-1}C_r &=\frac{(n-1)!}{(r-1)!((n-1)-(r-1))!} +\frac{(n-1)!}{r!(n-1-r)!} \\ &=\frac{(n-1)!}{(r-1)!(n-r)!} +\frac{(n-1)!}{r!(n-r-1)!} \\ &=\frac{(n-1)!r}{r!(n-r)!} +\frac{(n-1)!(n-r)}{r!(n-r)!} \\ &=\frac{(n-1)!n}{r!(n-r)!} =\frac{n!}{r!(n-r)!} ={}_nC_r \end{aligned} \] 따라서 \({}_nC_r={}_{n-1}C_{r-1}+{}_{n-1}C_r\)이다. |
| math:mappingConfidence | 1.0 |
| math:pageStart | 157 |
| math:problem | textbook_problem:donga_vision_p117_03 |
| math:reviewStatus | reviewed |
| math:solutionKind | worked_solution |
| math:usesSolutionPattern | solution_pattern:combination_pascal_identity |