Hitunglah nilai dari: d. 5​P2​7​P4​​

Pertanyaan

Hitunglah nilai dari:

d. begin mathsize 14px style fraction numerator straight P presubscript 7 subscript 4 over denominator straight P presubscript 5 subscript 2 end fraction end style 

R. Azizatul

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

nilai dari begin mathsize 14px style fraction numerator straight P presubscript 7 subscript 4 over denominator straight P presubscript 5 subscript 2 end fraction end style adalah 42.

Pembahasan

Gunakan konsep permutasi dan faktorial sebagai berikut:

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

sehingga:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator straight P presubscript 7 subscript 4 over denominator straight P presubscript 5 subscript 2 end fraction end cell equals cell fraction numerator begin display style fraction numerator 7 factorial over denominator open parentheses 7 minus 4 close parentheses factorial end fraction end style over denominator begin display style fraction numerator 5 factorial over denominator open parentheses 5 minus 2 close parentheses factorial end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 7 factorial over denominator 3 factorial end fraction end style over denominator begin display style fraction numerator 5 factorial over denominator 3 factorial end fraction end style end fraction end cell row blank equals cell fraction numerator 7 factorial over denominator 3 factorial end fraction cross times fraction numerator 3 factorial over denominator 5 factorial end fraction end cell row blank equals cell fraction numerator 7 factorial over denominator 5 factorial end fraction end cell row blank equals cell fraction numerator 7 times 6 times 5 factorial over denominator 5 factorial end fraction end cell row blank equals 42 end table end style  

Dengan demikian nilai dari begin mathsize 14px style fraction numerator straight P presubscript 7 subscript 4 over denominator straight P presubscript 5 subscript 2 end fraction end style adalah 42.

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