Practice - Combined Use of Sum and Product Rule
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Practice Questions
Test your understanding with targeted questions
How many ways can 3 students be chosen from a set of 5?
💡 Hint: Use C(n, k) = n! / (k!(n-k)!), where n is the total number and k is the number of choices.
If each student can pick one of 4 different books, how many choices are there for 3 students?
💡 Hint: Use the Product Rule: 4^3.
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Interactive Quizzes
Quick quizzes to reinforce your learning
How many ways can 2 employees be assigned to 3 different offices if they cannot share an office?
💡 Hint: Recall the Product Rule.
Is it true that if you have 15 items in 10 boxes, at least one box must contain more than one item?
💡 Hint: Think about how distribution must work.
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Challenge Problems
Push your limits with advanced challenges
In a network of 7 friends, where each pair is either friends or enemies, determine the minimum number of people needed to guarantee 3 mutual relationships.
💡 Hint: Visualize relationships as graphs.
For valid passwords of lengths 6, 7, and 8 using specified character sets, solve for total valid combinations accounting for at least one digit.
💡 Hint: Group by length for efficient counting.
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Reference links
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