A panel of 3 women and 4 men is to be formed from 8 women and 7 men.Find the number of ways which the panel can be formed if it must contain at least 2 women.


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Question Number 35640 by NECx last updated on 21/May/18

$A p a n e l o f 3 w o m e n a n d 4 m e n i s$ $t o b e f o r m e d f r o m 8 w o m e n a n d$ $7 m e n . F i n d t h e n u m b e r o f w a y s$ $w h i c h t h e p a n e l c a n b e f o r m e d i f$ $i t m u s t c o n t a i n a t l e a s t 2 w o m e n .$
	Answered by tanmay.chaudhury50@gmail.com last updated on 21/May/18

	$W = 8 M = 7 p a n e l (W 3 + M 4)$ $C_{3}^{8} \times C_{4}^{7}$ $i n f i r s t s e n t e n c e i t i s s a i d t h a t p s n e l (W 3 + M 4$ $i n l a s t s e n t e n c e p a n e l c o n t a i n a t l e a s t 2 W$ $s o w h e n n u m b e r o f w o m a n i n p a n e l i s f i x e d 3$ $t h e n h o w t h e t e r m a t l e s s t a p p e a r i n q u e s t i o n$ $p l s c h e c k . . . .$ $i f s o t h e n$ $C_{2}^{8} \times C_{4}^{7} + C_{3}^{8} \times C_{4}^{7}$
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