Jaylin has a wooden cube which is painted blue on the outside. She cuts the cube into 1000 identical cubes, some of which have some sides painted blue, then rolls the resulting cubes like dice. The probability that 1000 blue faces land up after Jaylin rolls the 1000 cubes can be expressed as 2^a \times 3^b \times 5^c where a, b and c are integers. What is the value of a + b + c?

sandwich May 13, 2023