bantuin ya pk cara gengerti makasih ya

Mapel : Matematika
Kelas : XII SMA
Bab : Peluang

Pembahasan :
Bnyak cara memilih 3 pria dari 9 pria
= 9C3
= 9!/(9 - 3)!3!
= 9!/6!3!
= (9 x 8 x 7)/6
= 84

n(s) = (9 + 7)C(3 + 2)
n(s) = 16C5
n(s) = 16!/(16 - 5)!5!
n(s) = 16!/11!5!
n(s) = 4368

Banyak cara memilih 2 wanita dari 7 wanita adlah ...
= 7C2
= 7!/(7 - 2)!2!
= 7!/5!2!
= 21

Maka...
P = n(k)/n(s)
P = (84 x 21)/4368
P = 21/52

[tex]\displaystyle P(A)=\frac{n(A)}{n(S)}\\P(A)=\frac{^{9}\text{C}_3\cdot{^7\text{C}_2}}{^{16}\text{C}_5}\\P(A)=\frac{\frac{9!}{3!6!}\cdot\frac{7!}{2!5!}}{\frac{16!}{5!11!}}\\P(A)=\frac{\frac{9\cdot8\cdot7}{3\cdot2}\cdot\frac{7\cdot6}{2}}{\frac{16\cdot15\cdot14\cdot13\cdot12}{5\cdot4\cdot3\cdot2}}\\P(A)=\frac{3\cdot4\cdot7\cdot7\cdot3}{2\cdot14\cdot13\cdot12}\\P(A)=\frac{3\cdot7}{13\cdot4}\\\boxed{\boxed{P(A)=\frac{21}{52}}}[/tex]