If a number is chosen at random from out of the four digited numbers formed by using the digits 0 , 1 , 2 , 3 , 4 , 6 without repetition, then the probability that it is divisible by 4 , is

Question

If a number is chosen at random from out of the four digited numbers formed by using the digits 0 , 1 , 2 , 3 , 4 , 6 without repetition, then the probability that it is divisible by 4 , is, 100 17 ​, 50 17 ​, 50 13 ​, 25 13 ​

MARKS App · Accepted Answer

If the number divisible by 4 using digits 0,1 , 2 , 3 , 4 , 6 unit place digit is even. Case I. If unit digit is 0 , then tens place possible digits is 2 , 4 , 6 Possible outcome = 4 × 3 × 3 = 36 Case II. If unit digit is 2 , then tens place digits are 1 and 3 Possible outcomes $ = 3 × 3 × 2 = 18 im g src = " h ttp s : // c d n − q u es t i o n − p oo l . g e t ma r k s . a pp / p y q / a p e ​ am ce t / o 8 Mp f c ​ NCQ c h o q mV s 6 r p h Z − L q 0 f O i L R I Vj X h q f 1 mV v Y . or i g ina l . f u ll s i ze . p n g " > b r > C a se III . I f u ni t d i g i t i s 4 , t h e n t e n s d i g i t s a re 0 , 2 an d 6. ( a ) I f t e n s d i g i t 0 P oss ib l e w a ys = 4 × 3 = 12 ( b ) I f t e n s d i g i t n o t zero , i . e . ( 2 an d 6 ) P oss ib l e w a ys = 3 × 3 × 2 = 18 im g src = " h ttp s : // c d n − q u es t i o n − p oo l . g e t ma r k s . a pp / p y q / a p e ​ am ce t / L 88 V 0 J h 4 i 3 M f v d u Hy R Y L − L 9 Wj I z 0 c B L 254 A 9 Q H p ​ 6 u E . or i g ina l . f u ll s i ze . p n g " > b r > S o , re q u i re d w a ys , i f u ni t d i g i t i s 4=18+12=30 . C a se I V . I f u ni t d i g i t i s 6 , t h e n d i g i t a re 1 an d 3 P oss ib l e w a ys im g src = " h ttp s : // c d n − q u es t i o n − p oo l . g e t ma r k s . a pp / p y q / a p e ​ am ce t / Kco n D ZPZCR n z SN L C u r R c f 2 I mk 8 g RTl 2 a y U b − D R Dy tS Y . or i g ina l . f u ll s i ze . p n g " > b r > He n ce , t o t a l n u mb ero f n u mb er w hi c hi s d i v i s ib l e b y 4=36+18+30+18 =102 N o w , t o t a l n u mb ero f w a yso ff or m f o u r d i g i t n u mb er u s in g 0,1,2,3,4,6 i s im g src = " h ttp s : // c d n − q u es t i o n − p oo l . g e t ma r k s . a pp / p y q / a p e ​ am ce t / A j d G N N ​ r N D x − y U o EE 8 bh r − a r G 6 J W gu t a D U 1 TSB 6 MtN g . or i g ina l . f u ll s i ze . p n g " > b r > T o t a l n u mb ero f 4 d i g i t n u mb er = 5 × 5 × 4 × 3 = 300 ∴ Required probability = 300 102 ​ = 50 17 ​ ​ $

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