Question

Jika C (n,r) menyatakan banyaknya kombinasi r elemendari n elemen dan C (n,3) = 2n, maka C (2n,7) =...

Answer 1

C(n, 3) = 2n
n!/(n - 3)!3! = 2n
n(n - 1)(n - 2)(n - 3)!/(n - 3)!.3.2.1 = 2n
n(n - 1)(n - 2)/6 = 2n
n(n² - 3n + 2) = 12n
n² - 3n + 2 = 12
n² - 3n - 10 = 0
(n - 5)(n + 2) = 0
n = 5 atau n = -2
dipilih n = 5
C(2n, 7) = C(10, 7) = 10!/(10-7)!.7! = (10. 9. 8. 7!) / (3 . 2 . 1 . 7!) = 120