A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits \(($\spadesuit$, $\heartsuit$, $\diamondsuit$,\) and $\(\clubsuit$ \)), such that there is exactly one card for any given rank and suit. Two of the suits \(($\spadesuit$ and $\clubsuit$) \) are black and the other two suits (\($\heartsuit$ and $\diamondsuit$)\) are red. The deck is randomly arranged. What is the probability that the top card is a \($\heartsuit$?\)
2.My three friends and I have dinner together every weekend. Each weekend, two of us cook and the other two clean up afterwards. How many different ways are there for us to choose who cooks and who cleans?
3.On the island of Mumble, the Mumblian alphabet has only $5$ letters, and every word in the Mumblian language has no more than $3$ letters in it. How many words are possible? (A word can use a letter more than once, but $0$ letters does not count as a word.)
4.A suitcase lock has 4 dials with the digits\( $0, 1, 2,..., 9$\) on each.