RoboguruRoboguru
SD

Tentukan nilai n jika diketahui : b. P2n​=10⋅P4n​

Pertanyaan

Tentukan nilai begin mathsize 14px style n end style jika diketahui :

b. begin mathsize 14px style straight P subscript 2 superscript n equals 10 times straight P subscript 4 superscript n end style 

 

S. Amamah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

nilai begin mathsize 14px style n end style yang memenuhi adalah 14. 

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 left parenthesis n minus 1 right parenthesis times left parenthesis n minus 2 right parenthesis times left parenthesis n minus 3 right parenthesis times left parenthesis n minus 4 right parenthesis times horizontal ellipsis end cell row cell straight P subscript r superscript n end cell equals cell fraction numerator n factorial over denominator left parenthesis n minus r right parenthesis 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 subscript 5 superscript n end cell equals cell 10 times straight P subscript 4 superscript n end cell row cell fraction numerator n factorial over denominator open parentheses n minus 5 close parentheses factorial end fraction end cell equals cell 10 times fraction numerator n factorial over denominator open parentheses n minus 4 close parentheses factorial end fraction end cell row cell fraction numerator n factorial over denominator open parentheses n minus 5 close parentheses factorial end fraction cross times fraction numerator open parentheses n minus 4 close parentheses factorial over denominator n factorial end fraction end cell equals cell 10 times fraction numerator n factorial over denominator left parenthesis n minus 4 right parenthesis factorial end fraction cross times fraction numerator left parenthesis n minus 4 right parenthesis factorial over denominator n factorial end fraction end cell row cell fraction numerator open parentheses n minus 4 close parentheses factorial over denominator open parentheses n minus 5 close parentheses factorial end fraction end cell equals 10 row cell fraction numerator open parentheses n minus 4 close parentheses times open parentheses n minus 5 close parentheses factorial over denominator open parentheses n minus 5 close parentheses factorial end fraction end cell equals 10 row cell n minus 4 end cell equals 10 row n equals 14 end table end style   

Dengan demikian nilai begin mathsize 14px style n end style yang memenuhi adalah 14. 

28

0.0 (0 rating)

Pertanyaan serupa

Nilai dari P(15,2)P(15,4)​ adalah....

1rb+

5.0

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia