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Diketahui: , maka nilai

Diketahui: large C subscript n superscript n plus 2 end superscript equals 45, maka nilai large P subscript n minus 6 end subscript superscript n minus large C subscript n minus 2 end subscript superscript n equals horizontal ellipsis  

  1. begin mathsize 14px style 22 end style 

  2. size 14px 24 

  3. size 14px 26 

  4. size 14px 28 

  5. size 14px 30 

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H. Endah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

jawaban yang benar adalah D.

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Pembahasan

Ingat rumus permutasi yaitu: dan rumus kombinasi yaitu: Diketahui , maka didapatkan: n ​ = ​ − 11 atau n = 8 ​ Nilai yang di ambil adalah karena di permutasi dan kombinasi nilai n tidak boleh negatif. Sehingga didapatkan: Dengan demikian,nilai . Jadi, jawaban yang benar adalah D.

Ingat rumus permutasi yaitu:

large P subscript r superscript n equals fraction numerator n factorial over denominator open parentheses n minus r close parentheses factorial end fraction 

dan rumus kombinasi yaitu:

large 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  

Diketahui large C subscript n superscript n plus 2 end superscript equals 45, maka didapatkan:

table attributes columnalign right center left columnspacing 0px end attributes row cell large C subscript n superscript n plus 2 end superscript end cell equals 45 row cell fraction numerator open parentheses n plus 2 close parentheses factorial over denominator open parentheses open parentheses n plus 2 close parentheses minus n close parentheses factorial times n factorial end fraction end cell equals 45 row cell fraction numerator open parentheses n plus 2 close parentheses factorial over denominator open parentheses n plus 2 minus n close parentheses factorial times n factorial end fraction end cell equals 45 row cell fraction numerator open parentheses n plus 2 close parentheses times open parentheses n plus 1 close parentheses times up diagonal strike n factorial end strike over denominator 2 factorial times up diagonal strike n factorial end strike end fraction end cell equals 45 row cell fraction numerator open parentheses n plus 2 close parentheses times open parentheses n plus 1 close parentheses over denominator 2 times 1 end fraction end cell equals 45 row cell fraction numerator n squared plus n plus 2 n plus 2 over denominator 2 end fraction end cell equals 45 row cell fraction numerator n squared plus 3 n plus 2 over denominator 2 end fraction end cell equals 45 row cell n squared plus 3 n plus 2 end cell equals cell 45 times 2 end cell row cell n squared plus 3 n plus 2 end cell equals 90 row cell n squared plus 3 n plus 2 minus 90 end cell equals 0 row cell n squared plus 3 n minus 88 end cell equals 0 row cell open parentheses n plus 11 close parentheses open parentheses n minus 8 close parentheses end cell equals 0 end table   

 

Nilai yang di ambil adalah begin mathsize 14px style n equals 8 end style karena di permutasi dan kombinasi nilai  tidak boleh negatif. Sehingga didapatkan:

table attributes columnalign right center left columnspacing 0px end attributes row cell large P subscript n minus 6 end subscript superscript n minus large C subscript n minus 2 end subscript superscript n end cell equals cell large P subscript 8 minus 6 end subscript superscript 8 minus large C subscript 8 minus 2 end subscript superscript 8 end cell row blank equals cell large P subscript 2 superscript 8 minus large C subscript 6 superscript 8 end cell row blank equals cell fraction numerator 8 factorial over denominator open parentheses 8 minus 2 close parentheses factorial end fraction minus fraction numerator 8 factorial over denominator open parentheses 8 minus 6 close parentheses factorial times 6 factorial end fraction end cell row blank equals cell fraction numerator 8 factorial over denominator 6 factorial end fraction minus fraction numerator 8 factorial over denominator 2 factorial times 6 factorial end fraction end cell row blank equals cell fraction numerator 8 cross times 7 cross times up diagonal strike 6 factorial end strike over denominator up diagonal strike 6 factorial end strike end fraction minus fraction numerator begin display style stack up diagonal strike 8 with 4 on top end style times 7 times up diagonal strike 6 factorial end strike over denominator up diagonal strike 2 times 1 times up diagonal strike 6 factorial end strike end fraction end cell row blank equals cell 56 minus 28 end cell row blank equals 28 end table  

Dengan demikian, nilai large P subscript n minus 6 end subscript superscript n minus large C subscript n minus 2 end subscript superscript n equals 28.  

Jadi, jawaban yang benar adalah D.

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