Kombinasi: Perbedaan antara revisi

Istilah '''kombinasi''' dalam [[Kombinatorika|matematika kombinatorik]] berarti [[himpunan]] objek yang tidak mementingkan urutan. Kombinasi berbeda dengan [[permutasi]] yang mementingkan urutan objek. Perkataan '''kombinasi''' memiliki sebutan lainnya yaitu '''gabungan''', '''padu-padan''' atau '''kepadupadanan'''

: <math>C^{12}_3 = \frac{12!}{3! (12-3)!} = \frac{12!}{3! 9!} = \frac{12 \cdot 11 \cdot 10 \cdot 9!}{3 \cdot 2 \cdot 1 \cdot 9!} = 220 cara</math> cara

;: <math>C^{5}_3 + C^{4}_3 + C^{3}_3 = \frac{5!}{3! (5-3)!} + \frac{4!}{3! (4-3)!} + \frac{3!}{3! (3-3)!} = \frac{5!}{3! 2!} + \frac{4!}{3! 1!} + \frac{3!}{3! 0!} = \frac{5 \cdot 4 \cdot 3!}{2 \cdot 1 \cdot 3!} + \frac{4 \cdot 3!}{1 \cdot 3!} + \frac{3!}{1 \cdot 3!} = 10 + 4 + 1 = 15 cara</math> cara

;: <math>C^{5}_1 \cdot C^{4}_1 \cdot C^{3}_1 = \frac{5!}{1! (5-1)!} \cdot \frac{4!}{1! (4-1)!} \cdot \frac{3!}{1! (3-1)!} = \frac{5!}{1! 4!} \cdot \frac{4!}{1! 3!} \cdot \frac{3!}{1! 2!} = \frac{5 \cdot 4!}{1 \cdot 4!} \cdot \frac{4 \cdot 3!}{1 \cdot 3!} \cdot \frac{3 \cdot 2!}{1 \cdot 2!} = 5 \cdot 4 \cdot 3 = 60 cara</math> cara

;: <math>C^{5}_2 \cdot C^{4}_1 + C^{5}_2 \cdot C^{3}_1 + C^{4}_2 \cdot C^{5}_1 + C^{4}_2 \cdot C^{3}_1 + C^{3}_2 \cdot C^{5}_1 + C^{3}_2 \cdot C^{4}_1
= \frac{5!}{32! (5-32)!} +\cdot \frac{4!}{31! (4-31)!} + \frac{35!}{32! (35-32)!} =\cdot \frac{53!}{31! 2(3-1)!} + \frac{4!}{32! 1(4-2)!} +\cdot \frac{35!}{31! 0(5-1)!} =+ \frac{5 \cdot4!}{2! (4-2)!} \cdot \frac{3!}{2 \cdot 1! \cdot (3-1)!} + \frac{43!}{2! (3-2)!} \cdot 3\frac{5!}{1! \cdot 3(5-1)!} + \frac{3!}{1 \cdot2! (3-2)!} = 10 +\cdot \frac{4 + !}{1! = 15 cara</math>(4-1)!}