Kombinasi: Perbedaan antara revisi

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Akuindo (bicara | kontrib)
Akuindo (bicara | kontrib)
Baris 177:
; <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>
** dua diantaranya sama
; <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!}{3! (3-2)!} \cdot 3\frac{5!}{1! \cdot 3(5-1)!} + \frac{3!}{1 \cdot3! (3-2)!} = 10 +\cdot \frac{4 + !}{1! = 15 cara</math>(4-1)!}
= \frac{5!}{2! 3!} \cdot \frac{4!}{1! 3!} + \frac{5!}{2! 3!} \cdot \frac{3!}{1! 2!} + \frac{4!}{2! 2!} \cdot \frac{5!}{1! 4!} + \frac{4!}{2! 2!} \cdot \frac{3!}{1! 2!} + \frac{3!}{2! 1!} \cdot \frac{5!}{1! 4!} + \frac{3!}{2! 1!} \cdot \frac{4!}{1! 3!}
= \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>
 
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