Tolong dijawab ya. 5 kombinasi 2. 4 kombinasi 1. 12 kombinasi 3 = ....

Tolong dijawab ya. 5 kombinasi 2. 4 kombinasi 1. 12 kombinasi 3 = ….

Jawaban Terkonfirmasi

Perkalian kombinasi:
$$begin{align}_5C_2times,_4C_1times,_{12}C_3&=frac{5!}{(5-2)!2!}timesfrac{4!}{(4-1)!1!}timesfrac{12!}{(12-3)!3!} \ &=frac{5!}{3!2!}timesfrac{4!}{3!}timesfrac{12!}{9!3!} \ &=frac{5.4.3!}{3!times 2}timesfrac{4.3!}{3!}timesfrac{12.11.10.9!}{9!times3.2.1} \ &=frac{5times 4}{2}times 4timesfrac{12times 11times 10}{3times 2} \ &=frac{20}{2}times 4times2times 11times 10 \ &=10times 8times 110 \ &=10times 880 \ &=8800end{align}$

Jawaban Terkonfirmasi

5C2 x 4C1 x 12C3
= 5!/3!.2! x 4!/3!.1! x 12!/9!.3!
= 5.4.3!/3!.2! x 4.3!/3!.1! x 12.11.10.9!/9!.3!
= 5.4/2 x 4/1 x 12.11.10.9!/9!.3!
= 20/2 x 4 x 12.11.10/3!
= 10 x 4 x 1320/3.2.1
= 40 x 1320/6
= 40 x 220
= 8800