Question

Hitung nilai n pada pers-pers berikut ini !

Answer 1

A. (n + 1)C4 = nC3
(n + 1)! / (n - 3)! . 4! = n! / (n - 3)! . 3!
(n + 1).n.(n - 1) (n - 2) / 24 = n(n - 1)(n - 2) / 6
(n + 1).n.(n - 1) (n - 2) = 4n(n - 1)(n - 2)
n + 1 = 4
n = 3

b. nC3 = 7n
n! / (n - 3)! . 3! = 7n
n(n - 1)(n - 2) / 6 = 7n
n(n - 1)(n - 2) = 42n
n² - 3n + 2 = 42
n² - 3n - 40 = 0
(n - 8) (n + 5) = 0
n = 8,-5
n = 8 karena positif jadi memenuhi

c. (n + 1)C3 = 4 . nC2
(n + 1)! / (n - 2)! . 3! = 4 . n! / (n - 2)! . 2!
(n + 1).n.(n - 1) / 6 = 4 . n(n - 1) / 2
(n + 1).n.(n - 1) = 12 . n(n - 1)
n + 1 = 12
n = 11