dari 10 orang siswa yang terdiri atas 7 orang putra

Ingat kembali rumus kombinasi berikut:

C subscript r superscript n equals fraction numerator n factorial over denominator open parentheses n minus r close parentheses factorial times r factorial end fraction comma space n greater than r

Diketahui dari 10 orang siswa yang terdiri dari 7 putra dan 3 putri akan dibentuk tim beranggotakan 5 orang. Jika diisyaratkan anggota tim tersebut paling banyak 2 putri, maka kemungkinannya:

  • 2 putri, 3 putra
  • 1 putri, 4 putra
  • 5 putra

Sehingga:

  • 2 putri, 3 putra

table attributes columnalign right center left columnspacing 0px end attributes row cell Banyak space tim end cell equals cell C subscript 2 superscript 3 times C subscript 3 superscript 7 end cell row blank equals cell fraction numerator 3 factorial over denominator 1 factorial times 2 factorial end fraction times fraction numerator 7 factorial over denominator 4 factorial times 3 factorial end fraction end cell row blank equals cell fraction numerator 3 times up diagonal strike 2 factorial end strike over denominator 1 times up diagonal strike 2 factorial end strike end fraction times fraction numerator 7 times up diagonal strike 6 times 5 times up diagonal strike 4 factorial over denominator up diagonal strike 4 factorial end strike times up diagonal strike 3 times up diagonal strike 2 times 1 end fraction end cell row blank equals cell 3 times 7 times 5 end cell row blank equals 105 end table

  • 1 putri, 4 putra

table attributes columnalign right center left columnspacing 0px end attributes row cell Banyak space tim end cell equals cell C subscript 1 superscript 3 times C subscript 4 superscript 7 end cell row blank equals cell fraction numerator 3 factorial over denominator 2 factorial times 1 factorial end fraction times fraction numerator 7 factorial over denominator 3 factorial times 4 factorial end fraction end cell row blank equals cell fraction numerator 3 times up diagonal strike 2 factorial end strike over denominator up diagonal strike 2 factorial end strike times 1 end fraction times fraction numerator 7 times up diagonal strike 6 times 5 times up diagonal strike 4 factorial end strike over denominator up diagonal strike 3 times up diagonal strike 2 times 1 times up diagonal strike 4 factorial end strike end fraction end cell row blank equals cell 3 times 7 times 5 end cell row blank equals 105 row blank blank blank end table

  • 5 putra

table attributes columnalign right center left columnspacing 0px end attributes row cell Banyak space tim end cell equals cell C subscript 5 superscript 7 end cell row blank equals cell fraction numerator 7 factorial over denominator 2 factorial times 5 factorial end fraction end cell row blank equals cell fraction numerator 7 times up diagonal strike 6 cubed times up diagonal strike 5 factorial end strike over denominator up diagonal strike 2 times 1 times up diagonal strike 5 factorial end strike end fraction end cell row blank equals cell 7 times 3 end cell row blank equals 21 row blank blank blank end table

table attributes columnalign right center left columnspacing 0px end attributes row cell Banyak space tim space keseluruhan space end cell equals cell space 105 plus 105 plus 21 end cell row blank equals 231 end table

Jadi, jawaban yang benar adalah D.

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