1. A list of four digits is selected at random from the set {0, 1, 2, 3, 4, 5, 6

Question

1. A list of four digits is selected at random from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. What is the probability that the four digits will be distinct (all different)? What is the probability that no two consecutive digits will be the same?


2. There are twelve universities in the Atlantic Coast Conference. The Conference forms a committee with representatives from four universities. If these universities are chosen at random, what is the probability that none of the North Carolina schools (UNC-Chapel Hill, NC State, Duke, or Wake Forest) is included?

Explanation / Answer

1) Pr[4 distinct digits] = (10*9*8*7) / (10*10*10*10) = 0.504

2) Pr[no NC schools] = C(8,4) / C(12,4) = 70/495 0.1414

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