I gave 2 methods of arriving at the correct answer. You gave one method

of arriving at the wrong answer. I think we may be able to agree which

is better.

How are you defining "better"? My only purpose was to convince Roger of something mathematical, and quite frankly I could have written the solution to a quadratic equation and he would have been none the wiser. Your method, on the other hand, was rather overkill. I just could not be bothered to look up the equation for combinations and permutations.

Or are you proposing maths duels at dawn?