15 numbers are randomly chosen from U(0,1), what is the probability that the sum of largest four numbers is greater than 3.5?

 With[{f = OrderDistribution[{UniformDistribution[], 15}, #] &}, Probability[a + b + c + d > 3 + 1 / 2, {a \[Distributed] f[15], b \[Distributed] f[14], c \[Distributed] f[13], d\[Distributed] f[12]}]] 

Trouble is, it is very, very slow. I shut it down after 30 minutes. When I used NProbability it converged on the wrong answer but it did warn me with numerous error messages. Another CAS could do the above code but it also returned the same wrong answer. The right answer is supposed to be:

$\frac{224077804910008595}{584325558976905216} $

$\approx 0.383481094515780$

How do I do this using Mathematica?

15 numbers are randomly chosen from U(0,1), what is the probability that the sum of largest four numbers is greater than 3.5?

 With[{f = OrderDistribution[{UniformDistribution[], 15}, #] &}, Probability[a + b + c + d > 3 + 1 / 2, {a \[Distributed] f[15], b \[Distributed] f[14], c \[Distributed] f[13], d\[Distributed] f[12]}]] 

Trouble is, it is very, very slow. I shut it down after 30 minutes. When I used NProbability it converged on the wrong answer but it did warn me with numerous error messages. Another CAS could do the above code but it also returned the same wrong answer. The right answer is supposed to be (it at least agrees with a simulation):

$\frac{224077804910008595}{584325558976905216} $

$\approx 0.383481094515780$

How do I do this using Mathematica?