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Question Number 131828 by Salman_Abir last updated on 09/Feb/21

	Answered by liberty last updated on 09/Feb/21

	$20 = \frac{6!}{3! . 3!}$
	Commented by Salman_Abir last updated on 09/Feb/21

	$detail$
	Answered by mr W last updated on 09/Feb/21

	$w e c h o o s e t h r e e c h i l d r e n f o r t h r e e$ $r e d s h i r t s :$ $C_{3}^{6} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20$ $\Rightarrow a n s w e r (A)$
	Commented by mr W last updated on 09/Feb/21

	$a n o t h e r w a y$ $s a y i f a c h i l d r e c e i v e s a r e d s h i r t, h e$ $g e t s t h e n u m b e r ‘ ‘ 1^{″}, o t h e r w i s e h e$ $g e t s t h e n u m b e r ‘ ‘ 0^{″} .$ ${(1 + x)}^{6} = \underset{k = 0}{\sum^{6}} C_{k}^{6} x^{k}$ $t h e c o e f f i c i e n t o f x^{3} t e r m i s t h e$ $a n s w e r w h i c h i s C_{3}^{6} = 20 .$
	Commented by mr W last updated on 09/Feb/21

	$a n o t h e r w a y$ $t o a r r a n g e 3 r e d a n d 3 g r e e n s h i r t s$ $i n 6 p o s i t i o n s (w i t h r e p e t i t i o n)$ $\frac{6!}{3! 3!} = 20$
	Commented by malwan last updated on 09/Feb/21

	$1 + 6 x + 15 x^{2} + 20 x^{3} + 15 x^{4} + 6 x^{5} + x^{6}$ $I l o v e y o u m r W$ $t h a n k y o u s o m u c h s i r$
	Commented by mr W last updated on 09/Feb/21

	$t h a n k s t o y o u t o o s i r!$
	Commented by Salman_Abir last updated on 09/Feb/21

	$thanks$
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