23. For his calculus final exam, Dr. Channing, whose classes have a reputation for being very easy, gives his students 20 problems with their complete solutions, and tells them that he will choose 10 of them randomly for the final exam. Students who solve all 10 problems correctly will get an A, those who solve 9 correctly will get a B, and those who solve only 8 correctly will get a C. Dr. Channing told them that he does not give partial credit, and whoever solves fewer than 8 problems correctly, will get an F. Dolly, who has not studied calculus all semester, has no idea how to do any of the problems.

However, she finds enough time to memorize only the solutions to 12 of the problems.

What is the probability that she gets A, B, C and F, respectively?