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Sebuah panitia yang beranggota 4 orang akan dipili...

Sebuah panitia yang beranggota 4 orang akan dipilih dari kumpulan 4 pria dan 7 wanita. Jika dalam panitia itu diharuskan ada paling sedikit 2 wanita, maka banyaknya cara untuk membentuk panitia tersebut adalah ....

Jawaban:

Ada 3 kemungkinan yaitu:

1. 2 wanita dan 2 pria

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell banyak space cara end cell equals cell C subscript 2 superscript 7 cross times C subscript 2 superscript 4 end cell row blank equals cell fraction numerator 7 factorial over denominator open parentheses 7 minus 2 close parentheses factorial 2 factorial end fraction cross times fraction numerator 4 factorial over denominator open parentheses 4 minus 2 close parentheses factorial 2 factorial end fraction end cell row blank equals cell fraction numerator 7 factorial over denominator 5 factorial 2 factorial end fraction cross times fraction numerator 4 factorial over denominator 2 factorial 2 factorial end fraction end cell row blank equals cell fraction numerator 7 cross times 6 cross times 5 factorial over denominator 5 factorial 2 cross times 1 end fraction cross times fraction numerator 4 cross times 3 cross times 2 factorial over denominator 2 factorial 2 cross times 1 end fraction end cell row blank equals cell 21 cross times 6 end cell row blank equals 126 end table end style

2. 3 wanita dan 1 pria

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell banyak space cara end cell equals cell C subscript 3 superscript 7 cross times C subscript 1 superscript 4 end cell row blank equals cell fraction numerator 7 factorial over denominator open parentheses 7 minus 3 close parentheses factorial 3 factorial end fraction cross times fraction numerator 4 factorial over denominator open parentheses 4 minus 1 close parentheses factorial 1 factorial end fraction end cell row blank equals cell fraction numerator 7 factorial over denominator 4 factorial 3 factorial end fraction cross times fraction numerator 4 factorial over denominator 3 factorial 1 factorial end fraction end cell row blank equals cell fraction numerator 7 cross times 6 cross times 5 cross times 4 factorial over denominator 4 factorial 3 cross times 2 cross times 1 end fraction cross times fraction numerator 4 cross times 3 factorial over denominator 3 factorial 1 end fraction end cell row blank equals cell 35 cross times 4 end cell row blank equals 140 end table end style

3. 4 wanita

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell banyak space cara end cell equals cell C subscript 4 superscript 7 end cell row blank equals cell fraction numerator 7 factorial over denominator open parentheses 7 minus 4 close parentheses factorial 4 factorial end fraction end cell row blank equals cell fraction numerator 7 factorial over denominator 3 factorial 4 factorial end fraction end cell row blank equals cell fraction numerator 7 cross times 6 cross times 5 cross times 4 factorial over denominator 3 cross times 2 cross times 1 cross times 4 factorial end fraction end cell row blank equals 35 end table end style

Total didapat dengan menjumlahkan semua kemungkinan seperti berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px Banyak size 14px space size 14px cara size 14px space size 14px membentuk size 14px space size 14px panitia end cell size 14px equals cell size 14px 126 size 14px plus size 14px 140 size 14px plus size 14px 35 end cell row blank size 14px equals cell size 14px 301 size 14px space size 14px cara end cell end table

Jadi, banyaknya cara untuk membentuk panitia tersebut adalah 301 cara.

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