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(x)=x^2 −4x+6


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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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