Question

how many five digit positive integers that are divisible by 4 can be formed using the digits 0 1 2 3 4 and 5 without any of the digits getting repeated in a number​

Answer 1

Given : five digit positive integers   divisible by 4   formed using the digits 0 1 2 3 4 and 5 without any of the digits getting repeated in a number​

To find : How Many numbers

Solution:

Any number is divisible by 4 if last two Digits are Divisible by 4

Last two Digits can be   12   , 20  , 24   , 32  ,   40    ,  52

Case  1  :  Last two Digit  12

1st Digit can be in 3 ways  3 , 4 , 5  (as 0 not possible as 1st Digit)

2nd Digit can be in 3 Ways  

3rd Digit can be in 2 Ways

3 * 3 * 2  = 18

Case  2  :  Last two Digit  20

then  4 * 3 * 2  =  24  

Case  3  :  Last two Digit  24

3 * 3 * 2  = 18

Case 4  :  Last two Digit  32

3 * 3 * 2  = 18

Case  5  :  Last two Digit  40

then  4 * 3 * 2  =  24  

Case  6  :  Last two Digit  52

3 * 3 * 2  = 18

= 4(18) + 2(24)

= 72 + 48

= 120

120  ,   5 Digit numbers are possible which are divisible by 4 and can be formed using 0 1 2 3 4 and 5 without any of the digits getting repeated in a number​

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