Hint: The probability that X of any n customers all have 2 for fewer items has a Binomial distribution with p = whatever (I think you need to double check your arithmetic on that, I get a slightly different answer).

Think about what has to happen for customer 15 to be the third to have 2 or fewer items. Then what has to happen for customer 3 to be the first and customer 15 to be the third?

Finally, apply the definition of conditional probability.