How many strings of seven hexadecimal digits do not have any repeated digits?   How many strings of seven hexadecimal digits have at least one repeated digit?   What is the probability that a randomly chosen string of seven hexadecimal digits has at least one repeated digit?

Four sisters all play on the same 12-person team. Three team captains are to be chosen at random. How many ways can the captains be chosen, in total? What is the probability that every one of the captains is one of the sisters?

A basket contains 6 white, 7 yellow, and 6 black transistors. If a transistor is randomly picked, find the probability that it is yellow. (Enter answer as a decimal with at least 4 correct decimal places)

5 coins are put in a bag. 3 of the coins are weighted with the probability of flipping heads being three times as great than the probability of flipping tails; the remaining coins are fair. One of these coins is selected at random and then flipped once. What is the probability that a weighted coin was selected given that heads was flipped? Write the answer as a fraction.