Question

Tentukan nilai n jika :
a.nC3=20C17
b.nP2=2.n-1P3
c.nC5=2.nC2
d.(n+1)P3=nP4

Answer 1

A.
n ! /(n-3)!  3!  = 20 C17
n(n-1)(n-2) = 3! 20 !/(3)! 17!
n(n-1)(n-2) = 20.19.18
n = 20

b.
nP2 = 2. (n-1)P3
n !/ (n-2)! = 2 . (n-1)! /(n-4)!
n !/(n-1)! = 2 (n-2)! /(n-4)!
n(n-1)!/(n-1)! = 2 (n-2)(n-3)(n-4)!/(n-4)!
n = 2(n-2)(n-3)
n = 2(n² -5n + 6)
n = 2n² -10n + 12
2n² - 11n + 12 = 0
(2n - 3)(n - 4)= 0
n = 3/2  atau n = 4
n ≥ 3 --> n = 4

c. n C5 =  2. nC2
n !/(n-5)! 5 ! = 2. n !/.(n-2)! . 2!
(n-2)! /(n-5)! = 2. 5!/2!
(n-2)(n-3)(n-4)  = 2x 5 x 4 x 3
(n-2)(n-3)(n-4) = 6 x 5 x 4
n - 2 = 6
n = 8

d.