Find the no of 10-digit nos. using the digits 0,1,2,3,4,5,6,7,8,9 without repetition. How many of these are divisible by 4?

dear jee king

number of 10 digit number is =9*9*8*7*6*5*4*3*2*1

number is divisible by 4  if its first 2 digit is divisible by 4(unit and 10th position)

 

at first two place digit can be  04,08,12,16,20,24,28,32,36,40,48,52,56,60,64,68,72,76,80,84,92,96

these are 22 possibilities out of these 6 possibilites include zero

case 1 zero is included in first two place

 total number ={8*7*6*5*4*3*2*1}*6

case 2 zero is not included

total number ={7*7*6*5*4*3*2*1} *16

 

so total number ={8*7*6*5*4*3*2*1}*6  +{7*7*6*5*4*3*2*1} *16

                        =8! *6  + 8! *14

                         =8! *20

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