Pertanyaan

3 ! × 3 ! × 3 ! × 3 ! ( 3 × 4 ) ! = ....

$\frac{( 3 \times 4 ) !}{3 ! \times 3 ! \times 3 ! \times 3 !} = ....$

$begin mathsize 14px style fraction numerator 4 factorial over denominator open parentheses 3 factorial close parentheses cubed end fraction end style$
$begin mathsize 14px style fraction numerator 12 factorial times 8 factorial times 5 over denominator 9 factorial cross times 6 factorial end fraction end style$
$begin mathsize 14px style fraction numerator 12 factorial times 8 factorial times 6 factorial over denominator 9 factorial cross times 6 factorial end fraction end style$
$begin mathsize 14px style fraction numerator 12 factorial times 9 factorial over denominator 8 factorial cross times 6 factorial end fraction end style$
$begin mathsize 14px style fraction numerator 12 factorial times 6 factorial over denominator 8 factorial cross times 8 factorial end fraction end style$

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Perhatikan perhitungan pada soal berikut ini. 3 ! × 3 ! × 3 ! × 3 ! ( 3 × 4 ) ! = = = = 6 × 6 × 6 × 6 12 ! 6 × 6 × 6 × 6 12 2 ⋅ 11 ⋅ 10 5 ⋅ 9 ⋅ 8 4 ⋅ 7 ⋅ 6 ⋅ 5 ! 2 ⋅ 11 ⋅ 5 ⋅ 4 ⋅ 7 ⋅ 5 ! 369.600 Kita cari pembagian faktorial pada opsi yang hasilnya sama dengan soal. Opsi A ( 3 ! ) 3 4 ! = = = ( 3 ! ) 2 ⋅ 3 ! 4 ⋅ 3 ! 36 4 9 1 Opsi B 9 ! × 6 ! 12 ! ⋅ 8 ! ⋅ 5 = = = 9 ! × 6 ! 12 ⋅ 11 ⋅ 10 ⋅ 9 ! ⋅ 8 ⋅ 7 ⋅ 6 ! ⋅ 5 12 ⋅ 11 ⋅ 10 ⋅ 8 ⋅ 7 ⋅ 5 369.600 Opsi C 9 ! × 6 ! 12 ! ⋅ 8 ! ⋅ 6 ! = = = 9 ! × 6 ! 12 ⋅ 11 ⋅ 10 ⋅ 9 ! ⋅ 8 ! ⋅ 6 ! 12 ⋅ 11 ⋅ 10 ⋅ 8 ! 53.222.400 Opsi D 8 ! × 6 ! 12 ! ⋅ 9 ! = = = 8 ! × 6 ! 12 ⋅ 11 ⋅ 10 ⋅ 9 ⋅ 8 ! ⋅ 9 ⋅ 8 ⋅ 7 ⋅ 6 ! 12 ⋅ 11 ⋅ 10 ⋅ 9 ⋅ 9 ⋅ 8 ⋅ 7 5.987.520 Opsi E 8 ! × 8 ! 12 ! ⋅ 6 ! = = = 8 ! × 8 ⋅ 7 ⋅ 6 ! 12 3 ⋅ 11 ⋅ 1 0 5 ⋅ 9 ⋅ 8 ! ⋅ 6 ! 7 3 ⋅ 11 ⋅ 5 ⋅ 9 7 1.485 Oleh karena itu, jawaban yang tepat adalah B.

Perhatikan perhitungan pada soal berikut ini.

$\frac{( 3 \times 4 ) !}{3 ! \times 3 ! \times 3 ! \times 3 !} = = = = \frac{12 !}{6 \times 6 \times 6 \times 6} \frac{12 ^{2} \cdot 11 \cdot 10 ^{5} \cdot 9 \cdot 8 ^{4} \cdot 7 \cdot 6 \cdot 5 !}{6 \times 6 \times 6 \times 6} 2 \cdot 11 \cdot 5 \cdot 4 \cdot 7 \cdot 5! 369.600$

Kita cari pembagian faktorial pada opsi yang hasilnya sama dengan soal.

Opsi A

$\frac{4 !}{( 3 ! ) ^{3}} = = = \frac{4 \cdot 3 !}{( 3 ! ) ^{2} \cdot 3 !} \frac{4}{36} \frac{1}{9}$

Opsi B

$\frac{12 ! \cdot 8 ! \cdot 5}{9 ! \times 6 !} = = = \frac{12 \cdot 11 \cdot 10 \cdot 9 ! \cdot 8 \cdot 7 \cdot 6 ! \cdot 5}{9 ! \times 6 !} 12 \cdot 11 \cdot 10 \cdot 8 \cdot 7 \cdot 5 369.600$

Opsi C

$\frac{12 ! \cdot 8 ! \cdot 6 !}{9 ! \times 6 !} = = = \frac{12 \cdot 11 \cdot 10 \cdot 9 ! \cdot 8 ! \cdot 6 !}{9 ! \times 6 !} 12 \cdot 11 \cdot 10 \cdot 8! 53.222.400$

Opsi D

$\frac{12 ! \cdot 9 !}{8 ! \times 6 !} = = = \frac{12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 ! \cdot 9 \cdot 8 \cdot 7 \cdot 6 !}{8 ! \times 6 !} 12 \cdot 11 \cdot 10 \cdot 9 \cdot 9 \cdot 8 \cdot 7 5.987.520$

Opsi E

$\frac{12 ! \cdot 6 !}{8 ! \times 8 !} = = = \frac{12 ^{3} \cdot 11 \cdot 1 0 ^{5} \cdot 9 \cdot 8 ! \cdot 6 !}{8 ! \times 8 \cdot 7 \cdot 6 !} \frac{3 \cdot 11 \cdot 5 \cdot 9}{7} \frac{1.485}{7}$

Oleh karena itu, jawaban yang tepat adalah B.

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