Pembahasan Ujian PAI: A20 – No. 28 – November 2016

Pembahasan Soal Ujian Profesi Aktuaris

SOAL
Banyaknya kombinasi dari \(k\) objek yang dipilih dari kumpulan \(n\) objek yang berbeda diberikan oleh \(\left( {\begin{array}{*{20}{c}} n\\ k \end{array}} \right)\). Tentukan persamaan yang tepat dari \(\left( {\begin{array}{*{20}{c}} n\\ k \end{array}} \right)\)

1. \(\left( {\begin{array}{*{20}{c}} n\\ k \end{array}} \right) = \left( {\begin{array}{*{20}{c}} {n – 1}\\ {k – 1} \end{array}} \right) + \left( {\begin{array}{*{20}{c}} {n – 1}\\ k \end{array}} \right)\)
2. \(\left( {\begin{array}{*{20}{c}} n\\ k \end{array}} \right) = \left( {\begin{array}{*{20}{c}} n\\ {k – 1} \end{array}} \right) + \left( {\begin{array}{*{20}{c}} {n – 1}\\ k \end{array}} \right)\)
3. \(\left( {\begin{array}{*{20}{c}} n\\ k \end{array}} \right) = \left( {\begin{array}{*{20}{c}} {n – 2}\\ {k – 2} \end{array}} \right) + \left( {\begin{array}{*{20}{c}} {n – 1}\\ k \end{array}} \right)\)
4. \(\left( {\begin{array}{*{20}{c}} n\\ k \end{array}} \right) = \left( {\begin{array}{*{20}{c}} {n – 1}\\ {k – 1} \end{array}} \right) + \left( {\begin{array}{*{20}{c}} {n – 1}\\ {k – 2} \end{array}} \right)\)
5. \(\left( {\begin{array}{*{20}{c}} n\\ k \end{array}} \right) = \left( {\begin{array}{*{20}{c}} {n – 1}\\ {k – 1} \end{array}} \right) – \left( {\begin{array}{*{20}{c}} {n – 1}\\ {k – 2} \end{array}} \right)\)

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