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total number of digits that can be formed are 4 *4! = 96 numbers divisible by 4 are --12= 2*2 =4 --04= 3*2= 6 --24= 2*2= 4 total = 14 hence numbers formed are 96-14 = 82 B
There are 5 Digits (0,1,2,3,4). How many 4 digit numbers formed by those digits(repetation not allowed) are not divisible by 4?
A.96 B.30 C.66 D.82 E.78
CONCEPT:For a Number to be divisible by 4, Number formed by Last two digits (Unit and tens) of the number MUST be divisible by 4
Last two digits of such 4 digit number may be _ _ 04 _ _ 12 _ _ 20 _ _ 24 _ _ 32 _ _ 40
Blue cases {3 cases 04, 20, 40} are similar cause they have used digit 0 in last two digits so number of ways to fill Thousands and hundred digits = 3*2 (3 choices for thousands and 2 choices for hundreds digits) = 6 ways i.e. Total cases = 3*6 = 18
Red cases {3 cases 12, 24, 32} are similar cause they have NOT used digit 0 in last two digits so number of ways to fill Thousands and hundred digits = 2*2 (2 choices for thousands cause 0 can't be taken there and 2 remaining choices for hundreds digits) = 4 ways i.e. Total cases = 3*4 = 12
Total Numbers divisible by 4 = 18+12 = 30 cases
Total 4 digit numbers using 5 Digits (0,1,2,3,4) = 4*4*3*2 = 96
There are 5 Digits (0,1,2,3,4). How many 4 digit numbers formed by those digits(repetation not allowed) are not divisible by 4?
A.96 B.30 C.66 D.82 E.78
Others:- TIME
to determine How many 4 digit numbers formed by those digits(repetation not allowed) are not divisible by 4 = TOTAL CASES- Total cases divisible by 4
for divisibility of 4 ; we need to have last two digits which are twice divisible by 2 ; in this case those two digits would be 12 , 20, 40,04,24, 32 and total possible cases would be ; 4*4*3*2*1 ; 96 for no divisible by 4 possible combinations case 1; when we have 20,40,04 ; 3*2*1*1*1 ; 6 *3 ; 18 case 2; when we have 12,24,32 ; 2*2*1*1* 1; 4*3 ; 12 total cases ; 18+12; 30 so digit numbers not divisible by 4 ; 96-30 ; 66 IMO C
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