Inviting friends from one side only: A man has 5 friends and his wife has 4 friends. They will invite friends from exactly one side (either his or hers), choosing one or more from that side. In how many ways can invitations be made?

Introduction / Context:
The phrase “either of their friends, one or more” is commonly interpreted to mean: choose a nonempty subset from exactly one side (his side or her side), but not a mixture. We count nonempty subsets from each side and add them.

Given Data / Assumptions:

• His friends: 5 distinct → nonempty subsets: 2^5 − 1 = 31.
• Her friends: 4 distinct → nonempty subsets: 2^4 − 1 = 15.
• Exactly one side is chosen.

Concept / Approach:

• Add the counts from the two disjoint choices (his side OR her side).

Step-by-Step Solution:

Verification / Alternative check:
If we had allowed mixing sides, the count would be 2^9 − 1 = 511, or (2^5 − 1)*(2^4 − 1) = 465 if at least one from each side. The given interpretation uniquely fits the provided options.

Why Other Options Are Wrong:

• 31 counts only his side; 18 or 9 arise from misinterpreting the constraint.
• “None of these” is false since 46 is correct under the stated interpretation.

Common Pitfalls:

• Including both sides simultaneously, which contradicts “either…one or more.”

Final Answer:
46