Q.

:•. Pembahasan

Faktorial merupakan suatu perkalian yang saling berurutan mulai dari faktor nilai n sampai dikali 1 ataupun sebaliknya. Faktorial ditandakan dengan tanda seru (!).

Bentuk Umum :

• n(n – 1)! atau n × … × 1

Contoh :

1! = 1 × 1 = 1

2! = 2 × 1 = 2

3! = 3 × 2 × 1 = 6

4! = 4 × 3 × 2 × 1 = 24

5! = 5 × 4 × 3 × 2 × 1 = 120

6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5.040

8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40.320

9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 362.880

10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3.628.800

:•. Penyelesaian

12! – 11! – 10! – 9!

= (12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) – (11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) – (10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) – (9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1))

= 479.001.600 – 39.916.800 – 3.628.800 – 362.880

= 439.084.800 – 3.628.800 – 362.880

= 442.713.600 – 362.880

= 442.350.720

_______________

:•. Kesimpulan

• Hasil dari 12! – 11! – 10! – 9! adalah 442.350.720

:•. Detail Jawaban

Mapel : Matematika

Kelas : 12 SMA

Materi : Kaidah pencacahan dan Faktorial

Bab : 7

Kode Soal : 2

Kode kategorasi : 12.2.7

faktorial

.

12!

= 12×11×10×9×8×7×6×5×4×3×2

= 479.001.600

11!

= 11×10×9×8×7×6×5×4×3×2

= 39.916.800

10!

= 10×9×8×7×6×5×4×3×2

= 3.628.800

9!

= 9×8×7×6×5×4×3×2

= 362.880

12! – 11! – 10! – 9!

= 479.001.600 – 39.916.800 – 3.628.800- 362.880

= 439.084.800 – 3.628.800 – 362.880

= 435.456.000 – 362.880

= 435.093.120