Question-131828

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