Aside from the 2 trivial answers, 0000x0=0000 and 1111x1=1111, there is one other answer. 1089*9=9801. You find C & E pretty quickly, as running through the digits 2-9 yields either impossible situations or results exceeding 4 digits. It takes similar trial and error to deduce the other two digits such that it works out.
You can do it in 6 ways: 11111x 1111x1 111x1x 11x111 1x1111 x11111 Each has the same probability: (1/6)5 x (5/6) = 1/6 x 1/6 x 1/6 x 1/6 x 1/6 x 5/6 = 5/46656 So the probability is 5/46656 x 6 = 5/7776 You can use the binomial theorem so answer more complex questions like these.