A number is divisble by four if the last two digits of the number are divisble by four. Using the digits 0 to 9 inclusive write an expression for the number of five digit numbers divisble by four...

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A number is divisble by four if the last two digits of the number are divisble by four. Using the digits 0 to 9 inclusive write an expression for the number of five digit numbers divisble by four that can be formed if a.) digits may be repeated b.) digits must not be repeated, by first listing all two digit number formed from the numbers 0 to 9 inclusive that can be divided by 4.

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(a) digits may be repeated ,first digit any 9 ,second digit 10,third digits 10  and last two digits can made divisible in 25 ways.

by fundamental principal counting

9 X10 X10X25=22500

(b) when unit digit 0

       9X8X7X4X1

when unit digit 2

   9X8X7X5X1

when unit digit 4

   9X8X7X5X1

when unit digit 6

   9X8X7X5X1

when unit digit 8

   9X8X7X5X1

Total numbers =9X8X7X4X1+4(9X8X7X5X1)

                     =504x(4+20)=504X24=12096

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