Ini gimana? (peluang)

16 orang = 9 pria dan 7 wanita
Dipilih 5 orang = 3 pria dan 2 wanita
n(A) = 9C3 . 7C2
= 9!/(9-3)!3! . 7!/(7-2)!2!
= (9.8.7.6!)/(6!3.2.1) . (7.6.5!)/(5!.2.1)
= (3.4.7) . (7.3)
= 1764
n(S) = 16C5
= 16!/(16-5)!5!
= (16.15.14.13.12.11!)/(11!.5.4.3.2.1)
= (16.15.14.13.12)/(15.8)
= 2.14.13.12
= 4368
Peluang = n(A)/n(S) = 1764/4368 = 21/52 = 294/728

[tex]\displaystyle 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]