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Hitunglah bentuk kombinasi berikut!

Pertanyaan

Hitunglah bentuk kombinasi berikut!

begin mathsize 14px style C presubscript 12 subscript 4 end style

Pembahasan Soal:

Rumus kombinasi begin mathsize 14px style k end style objek dari begin mathsize 14px style n end style objek yang berbeda, begin mathsize 14px style k less or equal than n end style yaitu

begin mathsize 14px style C presubscript n subscript k equals fraction numerator n factorial over denominator k factorial open parentheses n minus k close parentheses factorial end fraction end style

Berdasarkan rumus diatas maka diperoleh begin mathsize 14px style C presubscript 12 subscript 4 end style sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell C presubscript 12 subscript 4 end cell equals cell fraction numerator 12 factorial over denominator 4 factorial space open parentheses 12 minus 4 close parentheses factorial end fraction end cell row blank equals cell fraction numerator 12 factorial over denominator 4 factorial space 8 factorial end fraction end cell row blank equals cell fraction numerator 12 cross times 11 cross times 10 cross times 9 cross times 8 factorial over denominator 4 cross times 3 cross times 2 cross times 1 cross times 8 factorial end fraction end cell row blank equals cell fraction numerator 12 cross times 11 cross times 10 cross times 9 over denominator 4 cross times 3 cross times 2 cross times 1 end fraction end cell row blank equals cell fraction numerator 11 cross times 5 cross times 9 over denominator 1 end fraction end cell row blank equals 495 end table end style


Jadi, begin mathsize 14px style C presubscript 12 subscript 4 equals 495 end style.

 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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