I'll try my hand at this one........
For the first one......we are looking for a 2 digit number that is divisible by both 9 and 7.......since we are multipying this by 1000, the result will be divisible by the other integers 1-9.
This number, N, is 63
For the second one.......we need all the multiples of 63 between 100 - 1000.....these are
126, 189, 252, 315, 378, 441, 504, 567, 630, 693, 756, 819, 882, 945
For the third, there are 1000 possible outcomes for each dice roll.
For each of the above numbers - except 252, 441 and 882 - there are 3! = 6 outcomes that could produce that particular number......for example, the outcome 126 plus the rearrangement of the outcomes 162, 216, 261, 612, 621 would all produce 126 ......for 252, 441 and 882, there are just 3 identifiable outcomes associated with each of these numbers......for example, 252 , 225 and 552
So the probability that the dice could be rearranged to make one of the numbers is :
[11 * 6 + 3 *3] / 1000 = [66 + 9] / 1000 = 75/1000 = 3/40
That's my best shot.....!!!!!
