A man invite 5 friends choosen from 10 for a diner. He don′t want that two of them took part to that diner. The number of ways to choose her friends is: a)296 b)196 c)5 d)252


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Question Number 139741 by mathocean1 last updated on 30/Apr/21

$A m a n i n v i t e 5 f r i e n d s c h o o s e n$ $f r o m 10 f o r a d i n e r . H e {d o n}^{'} t$ $w a n t t h a t t w o o f t h e m t o o k p a r t$ $t o t h a t d i n e r . T h e n u m b e r o f$ $w a y s t o c h o o s e h e r f r i e n d s i s :$ $a) 296$ $b) 196$ $c) 5$ $d) 252$
	Answered by mr W last updated on 01/May/21

	$A i s s e l e c t e d b u t B n o t : C_{4}^{8} w a y s$ $B i s s e l e c t e d b u t A n o t : C_{4}^{8} w a y s$ $b o t h A a n d B a r e n o t s e l e c t e d : C_{5}^{8} w a y s$ $t o t a l l y : 2 \times C_{4}^{8} + C_{5}^{8} = 196 w a y s .$ $o r$ $t o s e l e c t 5 f r o m 10 : C_{5}^{10} w a y s$ $m i n u s$ $b o t h A a n d B a r e s e l e c t e d : C_{3}^{8}$ $v a l i d : C_{5}^{10} - C_{3}^{8} = 196 w a y s$
	Commented by otchereabdullai@gmail.com last updated on 01/May/21

	$nice one!$
	Answered by mathocean1 last updated on 01/May/21

	$t h a n k s$
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