Suppose a sample space is a deck of \(52\) playing cards. Let set \(A=\{ \text{Aces} \}\) and \(B=\{ \text{Kings} \}\) and use a Venn diagram to show that \(A\) and \(B\) are mutually exclusive.

Use a Venn diagram to show the intersection of the set \(A=\{\text{Aces}\}\) and \(B=\{\text{Spades}\}\) from the sample space of a deck of playing cards.

Find the number of permutations of the letters in the set \(\{\text{E, N, G, L, I, S, H}\}\).

How many strings of letters can be made from the letters in the word FINAL, if no letter can be repeated?

How many ways are there for three people from the set \(\{\text{Pat, Diane, Tim, JoAnn}\}\) to win first, second, and third prize in a contest?

How many four-person committees can be selected from a set of \(7\) people?