Question

Determine the number of six-digit integers (no leading zeros) in which no digit may be repeated and divisible by 4?

Answer 1

I've tried solving this problem, but the result is different with the solution provided in the book... This is my way :

in order the number to be divisible by 4, the last two-digit must be divisible by 4, so the possibilities are (I've group them) (24,64,84,28,48,68), (20,40,60,80), (12,32,52,72,92,16,36,56,76,96) so I'll have three cases

the first case : the number of six-digits integer that divisible by 4: 7 x 7 x 6 x 5 x 3 x 2 = 8820

the second case: the number of six-digits integer that divisible by 4: 8 x 7 x 6 x 5 x 4 x 1 = 6720

the third case: the number of six-digits integer that divisible by 4: 7 x 7 x 6 x 5 x 5 x 2 = 14700

so, the total is 30240 but the answer provided in the book is 33,600

what I'm missing? Is this the correct approach?

Answer 2

04 08?

Answer 3

the second case: the number of six-digits integer that divisible by 4: 8 x 7 x 6 x 5 x 6= 10080

10080+ 14700+8820=33600

you were just missing 2 numbers

Answer 4

ahh..., I missed them...,
ok.., thank you... :)