Mr-Peter-has-4-children-x-are-in-class-C-and-y-are-in-class-D-x-1-and-y-1-Show-that-the-number-of-possibility-to-choose-at-random-and-simultaneous-2-children-in-same-class-verify-this-equation-p-

Question Number 97323 by mathocean1 last updated on 07/Jun/20

M r P e t e r h a s 4 c h i l d r e n . x a r e i n

c l a s s C a n d y a r e i n c l a s s D . x ⩾ 1 a n d

y ⩾ 1 . S h o w t h a t t h e n u m b e r o f p o s s i b i l i t y

t o c h o o s e a t r a n d o m a n d s i m u l t a n e o u s

2 c h i l d r e n i n s a m e c l a s s v e r i f y t h i s

e q u a t i o n p (x) = x^{2} - 4 x + 6

Answered by mr W last updated on 07/Jun/20

x i n c l a s s C, 4 - x i n c l a s s D .

p = C_{2}^{x} + C_{2}^{4 - x} = \frac{x (x - 1) + (4 - x) (4 - x - 1)}{2}

= x^{2} - 4 x + 6

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