Monkeys typing on Typewriters

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 \(\frac ab\) where \(a\) and \(b\) are co-prime positive integers. Find the remainder when \(a+b\) is divided by 1000?

Details and Assumptions

The typewriter consists of 26 buttons labelled \(a\) to \(z\), and no other buttons

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