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Question Number 54286 by Tinkutara last updated on 01/Feb/19

Commented by Tinkutara last updated on 01/Feb/19
Answers 4d 5b
Commented by mr W last updated on 05/Feb/19

$4 (b)$ $5 (d)$ $? ? ?$
	Answered by mr W last updated on 02/Feb/19

	$Q 4 :$ $n u m b e r o f n u m b e r s w i t h o n e d i g i t : C_{1}^{9}$ $n u m b e r o f n u m b e r s w i t h t w o d i g i t s : C_{2}^{9}$ $n u m b e r o f n u m b e r s w i t h 3 d i g i t s : C_{3}^{9}$ $. . . . . .$ $n u m b e r o f n u m b e r s w i t h 9 d i g i t s : C_{9}^{9}$ $\Rightarrow C_{1}^{9} + C_{2}^{9} + C_{3}^{9} + . . . + C_{9}^{9} = 2^{9} - 1 = 511$ $\Rightarrow (b)$
	Commented by Tinkutara last updated on 03/Feb/19
	But in this are these numbers included like 2.1222333666 2.888999 2.446888 or any others with repetitons?
	Commented by mr W last updated on 03/Feb/19

	$n o r e p e t i t i o n s i r . t h e q u e s t i o n r e q u e s t s$ $n o n - z e r o d i g i t s i n i n c r e a s i n g o r d e r .$ $2.1245 i s o k, b u t 2.12445 i s n o t o k .$ $i f r e p e t i t i o n s a r e a l l o w e d, t h e r e w o u d e$ $b e i n f i n i t e n u m b e r s, e . g . 2.12445,$ $2.124445, 2.1244445, e t c .$
	Answered by mr W last updated on 06/Feb/19

	$Q 5 :$ $3 + (k - 1) \times 3 = 93$ $\Rightarrow k = 31$ $\Rightarrow o p t i o n (d)$ $e x p l a n a t i o n :$ $s u c h t h a t t h e w o r d M A T c a n n o t b e f o r m e d,$ $o n l y o n e o r t w o d i f f e r e n t$ $l e t t e r s m a y b e s e l e c t e d . t h e r e a r e$ $f o l l o w i n g w a y s t o d o t h i s :$ $a l l k c o u p o n s c a r r y l e t t e r T : 1 w a y$ $a l l k c o u p o n s c a r r y l e t t e r A : 1 w a y$ $a l l k c o u p o n s c a r r y l e t t e r M : 1 w a y$ $Σ : 3 w a y s$ $k c o u p o n s w i t h l e t t e r s T a n d A :$ $1 c o u p o n l e t t e r T, k - 1 c o u p o n s l e t t e r A : 1 w a y$ $2 c o u p o n s l e t t e r T, k - 2 c o u p o n s l e t t e r A : 1 w a y$ $3 c o u p o n s l e t t e r T, k - 3 c o u p o n s l e t t e r A : 1 w a y$ $. . . . .$ $k - 1 c o u p o n s l e t t e r T, 1 c o u p o n l e t t e r A : 1 w a y$ $Σ : (k - 1) w a y s$ $s i m i l a r l y$ $k c o u p o n s w i t h l e t t e r s T a n d M :$ $Σ : (k - 1) w a y s$ $k c o u p o n s w i t h l e t t e r s A a n d M :$ $Σ : (k - 1) w a y s$ $t o t a l l y t h e r e a r e 3 + (k - 1) \times 3 w a y s$ $t o s e l e c t o n l y o n e o r t w o d i f f e r e n t$ $l e t t e r s .$ $3 + (k - 1) \times 3 = 3 k = 93$ $\Rightarrow k = 31$
	Commented by Tinkutara last updated on 05/Feb/19
	But sir no option is matching
	Commented by mr W last updated on 06/Feb/19

	$a n s w e r i s k = 31 . i . e . o p t i o n d .$ $p r o o f t h a t o p t i o n b i s w r o n g :$ $i f 5 c o u p o n s a r e s e l e c t e d, o n l y f o l l o w i n g$ $s e l e c t i o n s {c a n}^{'} t s p e l l t h e w o r d M A T :$ $A A A A A$ $M M M M M$ $T T T T T$ $A M M M M$ $A A M M M$ $A A A M M$ $A A A A M$ $A T T T T$ $A A T T T$ $A A A T T$ $A A A A T$ $M T T T T$ $M M T T T$ $M M M T T$ $M M M M T$ $t o t a l l y o n l y 15 w a y s, n o t 93 w a y s .$ $t h a t i s t o s a y a n s w e r i n b o o k i s w r o n g .$
	Commented by Tinkutara last updated on 06/Feb/19
	Thanks a lot Sir!
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