A chamber of commerce board has seven total members, drawn from a pool of twenty candidates. There are two stages in the board's election process. First, a president, secretary, and treasurer are chosen. After that, four members are chosen to be “at large” without any specific title or district. How many possible boards could be chosen?

Daisy wants to arrange four vases in a row outside of her garden. She has eight vases to choose from. How many vase arrangements can she make?

How many ordered samples of 5 cards can be drawn from a deck of 52 cards without replacement?

In how many ways can five different colored balls be arranged in a row?

Quantitative Comparison

3 cards are chosen from a standard 52-card deck.

Quantity A: The number of ways to choose 3 cards with replacement

Quantity B: The number of ways to choose 3 cards without replacement

In how many ways can 6 differently colored rose bushes be planted in a row that only has room for 4 bushes?