Hitunglah: a. 5 C 2 . 7 C 2 b. (8 C 4 . 5 C 2)/(13 C 6)

a. 210, b. 175/429

Pembahasan

Untuk menghitung nilai dari kombinasi:

a.  5 C 2 . 7 C 2
b.  (8 C 4 . 5 C 2)/(13 C 6)

Kita akan menggunakan rumus kombinasi C(n, k) = n! / (k! * (n-k)!)

a.  **5 C 2 . 7 C 2**
    *   5 C 2 = 5! / (2! * (5-2)!) = 5! / (2! * 3!) = (5 * 4 * 3!) / (2 * 1 * 3!) = (5 * 4) / 2 = 20 / 2 = 10
    *   7 C 2 = 7! / (2! * (7-2)!) = 7! / (2! * 5!) = (7 * 6 * 5!) / (2 * 1 * 5!) = (7 * 6) / 2 = 42 / 2 = 21
    *   Hasilnya: 10 * 21 = 210

b.  **(8 C 4 . 5 C 2) / (13 C 6)**
    *   8 C 4 = 8! / (4! * (8-4)!) = 8! / (4! * 4!) = (8 * 7 * 6 * 5 * 4!) / (4 * 3 * 2 * 1 * 4!) = (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1) = 1680 / 24 = 70
    *   5 C 2 = 10 (sudah dihitung di atas)
    *   13 C 6 = 13! / (6! * (13-6)!) = 13! / (6! * 7!) = (13 * 12 * 11 * 10 * 9 * 8 * 7!) / (6 * 5 * 4 * 3 * 2 * 1 * 7!) = (13 * 12 * 11 * 10 * 9 * 8) / (6 * 5 * 4 * 3 * 2 * 1) = 1.235.520 / 720 = 1716
    *   Hasilnya: (70 * 10) / 1716 = 700 / 1716
    *   Disederhanakan: 700 / 1716 = 175 / 429

Jadi, hasil perhitungannya adalah:
a. 210
b. 175/429