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Question Number 96780 by mr W last updated on 04/Jun/20

Commented by mr W last updated on 04/Jun/20

$n o b o d y u n d e r s t a n d s ?$
Commented by mathmax by abdo last updated on 04/Jun/20

$i understand \lim_{n \to \infty} P_{n} . . . ? perhaps a japan language . . .$
Commented by mr W last updated on 05/Jun/20

$A f t e r u s i n g t r a n s l a t i o n a p p I t h i n k$ $t h e q u e s t i o n i s :$ $I n a b o x t h e r e a r e 3 n w r i t e b a l l s a n d$ $2 n r e d b a l l s . T h r e e b a l l s a r e t a k e n f r o m$ $t h e b o x . I f P_{n} i s t h e p r o b a b i l i t y t h a t$ $2 w h i t e b a l l s a n d 1 r e d b a l l a r e t a k e n,$ $f i n d \lim_{n \to \infty} P_{n} = ? .$
Commented by john santu last updated on 05/Jun/20

$P_{n} = \frac{C (3 n, 2) \times C (2 n, 1)}{C (5 n, 3)}$ $= \frac{\frac{(3 n) (3 n - 1)}{2.1} \times \frac{2 n}{1}}{\frac{(5 n) (5 n - 1) (5 n - 2)}{3.2.1}}$ $= \frac{n (3 n) (3 n - 1)}{5 n (5 n - 1) (5 n - 2)} \times 6$ $\lim_{n \to \infty} \frac{{18 n}^{2} (3 n - 1)}{5 n (5 n - 1) (5 n - 2)} = \frac{54}{125}$
Commented by mr W last updated on 05/Jun/20

$c o r r e c t, t h a n k s!$
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