For ten points, identify this number, the probability of rolling a sum of 13 with two standard dice.
Pencil and paper ready. This number represents the expected value of the determinant of a 5 Ã— 5 matrix in which every element is randomly chosen from the set {−1,0,1}. If Alice and Bob each draw  ve cards from a deck of ten cards numbered one through ten, this number represents the number of distinct ways that their decks can sum to the same number.   If dice are constructed5           in the shape of each Platonic solid, and their faces are numbered in ascending order starting with one, this is the number of ways to roll a  ve on every die. For ten points, identify this number, the probability of rolling a sum of 13 with two standard dice.
Pencil and paper ready. This number represents the expected value of the determinant of a 5 Ã— 5 matrix in which every element is randomly chosen from the set {−1,0,1}. If Alice and Bob each draw  ve cards from a deck of ten cards numbered one through ten, this number represents the number of distinct ways that their decks can sum to the same number.   
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