A shelf holds seven mystery novels and eight biographies. Josie chooses either a mystery novel or a biography. Then Juan is to choose a mystery novel and a biography. In which case would Juan have the greater number of choices?

Choosing a biography first leaves more choices.

Explanation:

Mystery novel chosen first

We're left with 6 mystery novels and 8 biographies, giving:

$6 \times 8 = 48$ different sets of choices for a novel and a biography.

Biography chosen first

We're left with 7 mystery novels and 7 biographies, giving:

$7 \times 7 = 49$ different sets of choices for a novel and a biography.

Choosing a biography first leaves more choices.