Roboguru

Pertanyaan

Dalam suatu pelatnas sepak bola ada 4 pemain senior dan 12 pemain muda yang akan dibentuk tim utama untuk bermain di suatu pertandingan. Tentukan peluang terpilih paling banyak 3 pemain senior dalam tim tersebut.

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

Kemungkinan 1

Pemain terpilih 1 senior dan 10 pemain muda

n open parentheses s close parentheses equals blank subscript 16 C subscript 11 equals fraction numerator 16 factorial over denominator left parenthesis 16 minus 11 right parenthesis factorial 11 factorial end fraction equals fraction numerator 16 factorial over denominator 5 factorial 11 factorial end fraction equals fraction numerator 16 cross times 15 cross times 14 cross times 13 cross times 12 cross times 11 factorial over denominator 5 cross times 4 cross times 3 cross times 2 cross times 1 cross times 11 factorial end fraction equals 4368 n open parentheses 1 S close parentheses equals subscript 4 C blank presubscript 1 equals fraction numerator 4 factorial over denominator left parenthesis 4 minus 1 right parenthesis factorial 1 factorial end fraction equals fraction numerator 4 factorial over denominator 3 factorial 1 factorial end fraction equals fraction numerator 4 cross times 3 factorial over denominator 3 factorial 1 factorial end fraction equals fraction numerator 4 over denominator 1 factorial end fraction equals 4 n open parentheses 10 M close parentheses equals subscript 12 C blank presubscript 10 equals fraction numerator 12 factorial over denominator left parenthesis 12 minus 10 right parenthesis factorial 1 factorial end fraction equals fraction numerator 12 factorial over denominator 2 factorial 10 factorial end fraction equals fraction numerator 12 cross times 11 cross times 10 factorial over denominator 2 factorial 10 factorial end fraction equals fraction numerator 132 over denominator 2 factorial end fraction equals 66 P open parentheses 1 S comma 10 M close parentheses equals fraction numerator 4 blank cross times 66 over denominator 4368 end fraction equals 264 over 4368

Kemungkinan 2

Pemain terpilih 2 senior dan 9 pemain muda

n open parentheses s close parentheses equals blank subscript 16 C subscript 11 equals fraction numerator 16 factorial over denominator left parenthesis 16 minus 11 right parenthesis factorial 11 factorial end fraction equals fraction numerator 16 factorial over denominator 5 factorial 11 factorial end fraction equals fraction numerator 16 cross times 15 cross times 14 cross times 13 cross times 12 cross times 11 factorial over denominator 5 cross times 4 cross times 3 cross times 2 cross times 1 cross times 11 factorial end fraction equals 4368 n open parentheses 2 S close parentheses equals subscript 4 C equals presubscript 2 fraction numerator 4 factorial over denominator left parenthesis 4 minus 2 right parenthesis factorial 2 factorial end fraction equals fraction numerator 4 factorial over denominator 2 factorial 2 factorial end fraction equals fraction numerator 4 cross times 3 cross times 2 factorial over denominator 2 factorial 2 factorial end fraction equals fraction numerator 12 over denominator 2 factorial end fraction equals 6 n open parentheses 9 M close parentheses equals subscript 12 C equals presubscript 9 fraction numerator 12 factorial over denominator left parenthesis 12 minus 9 right parenthesis factorial 9 factorial end fraction equals fraction numerator 12 factorial over denominator 3 factorial 9 factorial end fraction equals fraction numerator 12 cross times 11 cross times 10 cross times 9 factorial over denominator 3 cross times 2 cross times 1 factorial 9 factorial end fraction equals 1320 over 6 equals 220 P open parentheses 2 S comma 9 M close parentheses equals fraction numerator 6 blank cross times 220 over denominator 4368 end fraction equals 1320 over 4368

 

Kemungkinan 3

Pemain terpilih 3 senior dan 8 pemain muda

undefined

 

Kemungkinan 4

Pemain terpilih 11 muda

n open parentheses s close parentheses equals blank subscript 16 C subscript 11 equals fraction numerator 16 factorial over denominator left parenthesis 16 minus 11 right parenthesis factorial 11 factorial end fraction equals fraction numerator 16 factorial over denominator 5 factorial 11 factorial end fraction equals fraction numerator 16 cross times 15 cross times 14 cross times 13 cross times 12 cross times 11 factorial over denominator 5 cross times 4 cross times 3 cross times 2 cross times 1 cross times 11 factorial end fraction equals 4368 n open parentheses 11 M close parentheses equals blank subscript 12 C subscript 11 equals fraction numerator 12 factorial over denominator left parenthesis 12 minus 11 right parenthesis factorial 11 factorial end fraction equals fraction numerator 12 factorial over denominator 1 factorial 11 factorial end fraction equals fraction numerator 12 cross times 11 factorial over denominator 1 factorial cross times 11 factorial end fraction equals 12 P open parentheses 11 M close parentheses equals 12 over 4368

Peluang paling banyak terpilih 3 pemain muda adalah

264 over 4368 plus 1320 over 4368 plus 1980 over 4368 plus 12 over 4368 equals 3576 over 4368 equals 447 over 546

 

Jadi peluang paling banyak terpilih 3 pemain muda adalah   447 over 546

205

0.0 (0 rating)

Pertanyaan serupa

Sebuah kantong berisi 7 kelereng merah, 5 kelereng biru, dan 4 kelereng hijau. Jika diambil 3 kelereng sekaligus secara acak, tentukan peluang terambil kelereng berbeda warna.

106

0.0

Jawaban terverifikasi

RUANGGURU HQ

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

Coba GRATIS Aplikasi Ruangguru

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