A tech conference schedules 6 speakers, including Alex, Bruno, Carla, and Denise, to give presentations in 6 different time slots, one speaker per slot. If Alex must speak earlier than Bruno, Bruno earlier than Carla, and Carla earlier than Denise, in how many different ways can the 6 speakers be scheduled?

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120

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Official Explanation

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The total number of ways of scheduling 6 speakers without constraints is

6!

.

We want a sequence where Alex speaks earlier than Bruno, Bruno earlier than Carla, and Carla earlier than Denise. That is just one specific relative order out of the

4!

possible relative orders of Alex, Bruno, Carla, and Denise within the total

6!

schedules.…

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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.