Pertanyaan

Terdapat sebuah kotak berisi 5 bola putih dan 6 bolah hitam. Joni mengambil 4 bola dari kotak tersebut. Banyak cara Joni mengambil maksimal 2 bola hitam adalah ....

R. Azizatul

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

total banyak caranya adalah 150 + 60 + 5 = 215.

Pembahasan

Beberapa kasus yang terjadi dengan maksimal 2 bola hitam adalah sebagai berikut: 2 bola putih dan 2 bola hitam, maka banyak caranya adalah 3 bola putih dan 1 bola hitam, maka banyak caranya adalah 4 bola putih, maka banyak caranya adalah Jadi, total banyak caranya adalah 150 + 60 + 5 = 215.

Beberapa kasus yang terjadi dengan maksimal 2 bola hitam adalah sebagai berikut:

2 bola putih dan 2 bola hitam, maka banyak caranya adalah

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight C presubscript 5 presuperscript straight subscript 2 space. space straight C presubscript 6 presuperscript straight subscript 2 end cell equals cell fraction numerator 5 factorial over denominator 3 factorial space. space 2 factorial end fraction space. space fraction numerator 6 factorial over denominator 4 factorial space. space 2 factorial end fraction end cell row blank equals cell fraction numerator 5 cross times 4 cross times 3 factorial over denominator 3 factorial space. space 2 factorial end fraction space. space fraction numerator 6 cross times 5 cross times 4 factorial over denominator 4 factorial space. space 2 factorial end fraction end cell row blank equals cell fraction numerator 5 cross times 4 cross times up diagonal strike 3 factorial end strike over denominator up diagonal strike 3 factorial end strike space. space 2 factorial end fraction space. space fraction numerator 6 cross times 5 cross times up diagonal strike 4 factorial end strike over denominator up diagonal strike 4 factorial end strike space. space 2 factorial end fraction end cell row blank equals cell fraction numerator 5 cross times 4 over denominator 2 factorial end fraction space. space fraction numerator 6 cross times 5 over denominator 2 factorial end fraction end cell row blank equals cell 20 over 2 space. space 30 over 2 end cell row blank equals cell 10 space. space 15 end cell row blank equals 150 end table end style$

3 bola putih dan 1 bola hitam, maka banyak caranya adalah

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight C presubscript 5 presuperscript straight subscript 3 space. space straight C presubscript 6 presuperscript straight subscript 1 end cell equals cell fraction numerator 5 factorial over denominator 2 factorial space. space 3 factorial end fraction space. space fraction numerator 6 factorial over denominator 5 factorial space. space 1 factorial end fraction end cell row blank equals cell fraction numerator 5 cross times 4 cross times 3 factorial over denominator 2 factorial space. space 3 factorial end fraction space. space fraction numerator 6 cross times 5 factorial over denominator 5 factorial space. space 1 factorial end fraction end cell row blank equals cell fraction numerator 5 cross times 4 cross times up diagonal strike 3 factorial end strike over denominator 2 factorial space. space up diagonal strike 3 factorial end strike end fraction space. space fraction numerator 6 cross times up diagonal strike 5 factorial end strike over denominator up diagonal strike 5 factorial end strike bullet 1 factorial end fraction end cell row blank equals cell fraction numerator 5 cross times 4 over denominator 2 factorial end fraction space. space fraction numerator 6 over denominator 1 factorial end fraction end cell row blank equals cell 20 over 2 space. space 6 over 1 end cell row blank equals cell 10 space. space 6 end cell row blank equals 60 end table end style$

4 bola putih, maka banyak caranya adalah

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight C presubscript 5 presuperscript straight subscript 4 end cell equals cell fraction numerator 5 factorial over denominator 1 factorial space. space 4 factorial end fraction end cell row blank equals cell fraction numerator 5 cross times 4 factorial over denominator 1 factorial space. space 4 factorial end fraction end cell row blank equals cell fraction numerator 5 cross times up diagonal strike 4 factorial end strike over denominator 1 factorial space. space up diagonal strike 4 factorial end strike end fraction end cell row blank equals cell fraction numerator 5 over denominator 1 factorial end fraction end cell row blank equals 5 end table end style$

Jadi, total banyak caranya adalah 150 + 60 + 5 = 215.

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