1first question ka answer will be 120
consider 5-digit numbers formed using the digits 0,1,2,3,4,5 without repetition of digits.
Q) the number of numbers divisible by 4 is ?
Q) the number of numbers divisible by 12 is?
Q) the number of numbers divisible by 15 is ?
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8 Answers
1my method:
i fixed last two digits as multiples of 4,and then found out the no of digits.
fixing multiples of 4,digits which do not have 0 in the last two digits are 12,24,32,52; which will give us a total
of (3*3*4*2)=72;
now ,considering last two digits containing 0's.i.e. 20&40,we have a total of (4!*2)=48 nos.
hence total such nos. possible=(72+48)=120 !
211. By similar process as Satyajit in for the cases having 24,12,32,52 are 72.
But in 2nd part 4 will divide the no. if it ends in 20,40 or 04. Then the no. of cases is 3(4P3)=72.
So, total nos. are 72+72=144
1057de first 1ne is 144 as explained by arnab...
for de 2nd de no has to be both divisible by 4 nd by 3....
so sum of de digits of de 5 digit no shud be divisible by 3....
only cases are:
1)12345
last 2 digits can be 12,32,52 and 24 nd de first 3 digits can be arranged in 3! ways in each case.....so 24 ways....
2)12450
last 2 digits can be 12,24,20,40,04,52....numbers ending with 20,40,04 can be arranged each in 3! ways so 18 ways...
nos ending in 12,24,52 can be arranged each in 4 ways so 12 ways...
so total 54 ways.....
3A number is divisible by 4 if its last 2 digits is divisible 4, which are 04,12,20,24,32,40,52.
The first 3 digits are the remaining digits excluding those with 0 as the first digit.
Total number is: 24*3+18*4=144.
A number is divisible by 12 if it is divisible by 3 and by 4.
A number is divisible by 3 if the sum of its digits is divisible by 3.
Last 2 digits 04 or 40, first 3 digits must be 1,2,5.
Last 2 digits 20 or 32, first 3 digits must be 1,4,5.
Last 2 digits 12, first 3 digits must be 0,4,5 or 3,4,5.
Last 2 digits 24, first 3 digits must be 0,1,5 or 1,3,5.
Last 2 digits 52, first 3 digits must be 0,1,4 or 1,3,4.
Total number is: 6*4+10*3=54
A number is divisible by 15 if it is divisible by 3 and by 5.
A number is divisible by 5 if its last digit is 0 or 5.
Last digit 0, first 4 digits must be 1,2,4,5.
Last digit 5, first 4 digits must be 0,1,2,4 or 1,2,3,4.
Total number is: 24+18=42