How many numbers greater than 200 can be formed from the digits 1,2,3,4,5 if no digit is to be repeated in any particular number?


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Question Number 151615 by pete last updated on 22/Aug/21

$How many numbers greater than 200 can$ $be formed from the digits 1, 2, 3, 4, 5 if no$ $digit is to be repeated in any particular$ $number ?$
	Answered by mr W last updated on 22/Aug/21

	$P_{3}^{5} - P_{2}^{4} + P_{4}^{5} + P_{5}^{5} = 288$
	Commented by pete last updated on 22/Aug/21

	$Thanks sir, but can you please explain$ $a little ?$
	Commented by mr W last updated on 22/Aug/21

	$3 - d i g i t n u m b e r s :$ $f r o m 5 d i g i t s y o u c a n f o r m P_{3}^{5} 3 - d i g i t$ $n u m b e r s . b u t t h e n u m b e r s b e g i n n i n g$ $w i t h 1 m u s t b e e x c l u d e d, b e c a u s e$ $t h e y a r e s m a l l e r t h a n 200 . w h e n a$ $n u m b e r b e g i n n t w i t h 1, t o f o r m t h e$ $n e x t 2 d i g i t s f r o m t h e o t h e r 4 d i g i t s,$ $t h e r e a r e P_{2}^{4} w a y s . t h e r e f o r e t h e r e$ $a r e P_{3}^{5} - P_{2}^{4} 3 - d i g i t n u m b e r s l a r g e r$ $t h a n 200 .$ $4 - d i g i t n u m b e r s :$ $t o f o r m a 4 - d i g i t n u m b e r f r o m 5$ $d i g i t s t h e r e a r e P_{4}^{5} w a y s . a l l t h e s e$ $n u m b e r s a r e l a r g e r t h a n 200 .$ $5 - d i g i t n u m b e r s :$ $t o f o r m a 5 - d i g i t n u m b e r f r o m 5$ $d i g i t s t h e r e a r e P_{5}^{5} w a y s . a l l t h e s e$ $n u m b e r s a r e l a r g e r t h a n 200 .$ $t o t a l l y w e c a n f o r m$ $P_{3}^{5} - P_{2}^{4} + P_{4}^{5} + P_{5}^{5} r e q u e s t e d n u m b e r s .$
	Commented by pete last updated on 26/Aug/21

	$Thank you sir$
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