Monkeys typing on Typewriters

There are 26 possibilities for each letter, and there are 6 letters so there are (26^6=308915776) different combinations that Lorcan the Monkey could have typed. Out of these combinations 1 of them is "lorcan" therefore the probability that he types out "lorcan" on the typewriter is $\frac{1}{308915776}$ So $a=1$ and $b=308915776$ . Therefore $a+b = 308915777$ . The remainder when $a+b$ is divided by 1000 is 777, so the answer is $\boxed{777}$

Each letter of "lorcan" has the probabilty of 1/26. Then the total probabilty is given by 1/26^6. Then we need to find x, when x=1+26^6(mod 1000), of this, x=777