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Question Number 55468 by peter frank last updated on 24/Feb/19

	Answered by mr W last updated on 25/Feb/19

	$t o c h o o s e 4 c h a r a c t e r s t h e r e a r e t h r e e$ $c a s e s :$ $c a s e 1 : t w o l e t t e r s, o n e d i g i t, o n e s y m b o l$ $t o c h o o s e 2 l e t t e r s t h e r e a r e C_{2}^{26} = 325 w a y s,$ $t o c h o o s e a d i g i t t h e r e a r e 9 w a y s,$ $t o c h o o s e a s y m b o l t h e r e a r e 5 w a y s,$ $t o t a l l y 325 \times 9 \times 5 = 14625 w a y s$ $c a s e 2 : o n e l e t t e r, t w o d i g i t s, o n e s y m b o l$ $t o c h o o s e 1 l e t t e r t h e r e a r e 26 w a y,$ $t o c h o o s e 2 d i g i t s t h e r e a r e C_{2}^{9} = 36 w a y s,$ $t o c h o o s e a s y m b o l t h e r e a r e 5 w a y s,$ $t o t a l l y 26 \times 36 \times 5 = 4680 w a y s$ $c a s e 3 : o n e l e t t e r, o n e d i g i t, t w o s y m b o l s$ $t o c h o o s e 1 l e t t e r t h e r e a r e 26 w a y,$ $t o c h o o s e 1 d i g i t t h e r e a r e 9 w a y s,$ $t o c h o o s e 2 s y m b o l s t h e r e a r e C_{2}^{5} = 10 w a y s,$ $t o t a l l y 26 \times 9 \times 10 = 2340 w a y s$ $\Rightarrow t o c h o o s e 4 c h a r a c t e r s t h e r e a r e$ $14625 + 4680 + 2340 = 21645 w a y s .$ $t o a r r a n g e e a c h 4 c h a r a c t e r s t h e r e$ $a r e 4! w a y s, t h e r e f o r e t o t a l n u m b e r$ $o f p a s s w o r d s w h i c h c a n b e f o r m e d i s$ $21645 \times 4! = 519480$
	Commented by peter frank last updated on 25/Feb/19

	$c o r r e c t s i r$
	Commented by mr W last updated on 25/Feb/19

	$s e e Q 55502 f o r a l t e r n a t i v e s o l u t i o n .$
	Commented by I want to learn more last updated on 04/Sep/20

	$Thank you sir$
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