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Solution: We compute the number of favorable outcomes: choosing 1 non-engagement proposal (from 3) and 2 engagement proposals (from 5).
Solution: Since the robot arms are identical, the problem reduces to choosing 4 distinct arms out of 6 to place the sensors. However, because the arms are indistinct, the order of placement does not matter. Thus, the number of ways is the number of combinations of 6 arms taken 4 at a time:
Question: A museum curator needs to display 7 vintage calculators in 4 identical glass cases, ensuring no case is empty. How many distinct arrangements are possible?

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