The International Group (IG) conference has just begun. This year, IG is hosting 4 distinguished speakers. Attendees can choose to sit in on or skip each lecture. How many minimum number of attendees would need to come to IG to guarantee that, at the end of the conference, at least two attendees will have sat in on and skipped exactly the same lectures all through the 4 speakers?

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Official Explanation

Official

Each attendee has 2 options for each lecture.

Hence, total different combinations possible =

2 \times 2 \times 2 \times 2 = 16

.

Since we want to guarantee that, at the end of the conference, at least two attendees will have sat in on and skipped exactly the same lectures all through the 4 speakers, total number of attendees must be equal to

16 + 1 = 17

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What this question tests

What it tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Common trap

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.