Soal kombinasi, hitunglah nilai 6n yang memenuhi persamaan berikut , 5 x c ((n-1),5) = 3 x c(n,4)

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Soal kombinasi


hitunglah nilai 6n yang memenuhi persamaan berikut
5 x c ((n-1),5) = 3 x c(n,4)​

Jawab:

5\times\frac{(n-1)!}{5!(n-1-5)!} =3\times\frac{n!}{4!(n-4)!}

\frac{5}{3}=\frac{n!}{(n-1)!} \times\frac{5!(n-6)!}{4!(n-4)!}

\frac{5}{3} =n\times\frac{5}{(n-4)(n-5)}

3n = (n-4)(n-5)

n^2-12n+20=0

(n-2)(n-10)=0

n₁ = 2 –> 6n₁ = 12

n₂ = 10 –> 6n₂ = 60

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