I have n independent trials, where the result of each trial is either A, B or C, with probabilities a, b and c respectively, so that a + b + c = 1.

What is the probability that all results are either A or B (in any combination/permutation, but no C), including at least one A and at least one B?

Is it a*b*(a+b)^(n-2)?

Or n*(n-1)*a*b*(a+b)^(n-2)?

Or something else?

Getting confused, please help!

What is the probability that all results are either A or B (in any combination/permutation, but no C), including at least one A and at least one B?

Is it a*b*(a+b)^(n-2)?

Or n*(n-1)*a*b*(a+b)^(n-2)?

Or something else?

Getting confused, please help!

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