Monkeys typing on Typewriters

Probability Level 2

Lorcan the monkey sits on a typewriter and types 6 letters randomly. The probability that he types out ``lorcan'' on the typewriter can be expressed as ab\frac ab where aa and bb are co-prime positive integers. Find the remainder when a+ba+b is divided by 1000?

Details and Assumptions

The typewriter consists of 26 buttons labelled aa to zz, and no other buttons

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