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SSAT Upper Level
Quantitative (Math)

Counting Unique Combinations in Talent Show

Hard Data Analysis And Probability Counting Methods

A school is organizing a talent show, and students can perform one of three types of acts: singing, dancing, or acting. Each act can feature a combination of up to 4 students. The school wants to know how many different combinations of acts they can form if:

1. All students are distinct individuals.

2. Each act can contain any number of students from 1 to 4.

3. A student cannot perform in multiple acts.

If there are 5 students available for the acts, how many unique combinations of acts can be formed?

Hint

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