Pertanyaan

Tunjukkan bahwa P ( n , r ) = r ! C ( n , r )

Tunjukkan bahwa  

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

terbukti bahwa

terbukti bahwa P left parenthesis n comma space r right parenthesis equals r factorial space C left parenthesis n comma space r right parenthesis 

Pembahasan

Ingat kembali bahwa Sehingga Jadi, terbukti bahwa

Ingat kembali bahwa 

P left parenthesis n comma space r right parenthesis equals fraction numerator n factorial over denominator left parenthesis n minus r right parenthesis factorial end fraction C left parenthesis n comma space r right parenthesis equals fraction numerator n factorial over denominator r factorial space left parenthesis n minus r right parenthesis factorial end fraction 

Sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell P left parenthesis n comma space r right parenthesis end cell equals cell r factorial space C left parenthesis n comma space r right parenthesis end cell row cell fraction numerator n factorial over denominator left parenthesis n minus r right parenthesis factorial end fraction end cell equals cell up diagonal strike r factorial end strike space cross times fraction numerator n over denominator up diagonal strike r factorial end strike space left parenthesis n minus r right parenthesis factorial end fraction end cell row blank equals cell fraction numerator n factorial over denominator left parenthesis n minus r right parenthesis factorial end fraction end cell end table 

Jadi, terbukti bahwa P left parenthesis n comma space r right parenthesis equals r factorial space C left parenthesis n comma space r right parenthesis 

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