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Hitunglah nilai dari: b. 8​P5​+4​P2​

Pertanyaan

Hitunglah nilai dari:

b. begin mathsize 14px style straight P presubscript 8 subscript 5 plus straight P presubscript 4 subscript 2 end style 

S. Amamah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

nilai dari begin mathsize 14px style straight P presubscript 8 subscript 5 plus straight P presubscript 4 subscript 2 end style adalah 6.732.

Pembahasan

Gunakan konsep permutasi dan faktorial sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell n factorial end cell equals cell n times open parentheses n minus 1 close parentheses times open parentheses n minus 2 close parentheses times open parentheses n minus 3 close parentheses times open parentheses n minus 4 close parentheses times horizontal ellipsis end cell row cell P subscript r superscript n end cell equals cell fraction numerator n factorial over denominator open parentheses n minus r close parentheses factorial end fraction comma space n greater than r end cell end table end style  

sehingga:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight P presubscript 8 subscript 5 plus straight P presubscript 4 subscript 2 end cell equals cell fraction numerator 8 factorial over denominator open parentheses 8 minus 5 close parentheses factorial end fraction plus fraction numerator 4 factorial over denominator open parentheses 4 minus 2 close parentheses factorial end fraction end cell row blank equals cell fraction numerator 8 factorial over denominator 3 factorial end fraction plus fraction numerator 4 factorial over denominator 2 factorial end fraction end cell row blank equals cell fraction numerator 8 times 7 times 6 times 5 times 4 times 3 factorial over denominator 3 factorial end fraction plus fraction numerator 4 times 3 times 2 factorial over denominator 2 factorial end fraction end cell row blank equals cell open parentheses 8 times 7 times 6 times 5 times 4 close parentheses plus open parentheses 4 times 3 close parentheses end cell row blank equals cell 6.720 plus 12 end cell row blank equals cell 6.732 end cell end table end style  

Dengan demikian nilai dari begin mathsize 14px style straight P presubscript 8 subscript 5 plus straight P presubscript 4 subscript 2 end style adalah 6.732.

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Tentukan nilai n jika diketahui pernyataan berikut ini. a.   10P(n,4)=P(n,5)

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