Practice Combined Use of Sum and Product Rule - 10.4 | 10. Basic Rules of Counting | Discrete Mathematics - Vol 2
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10.4 - Combined Use of Sum and Product Rule

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

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.

Question 2

Easy

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.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

How many ways can 2 employees be assigned to 3 different offices if they cannot share an office?

  • 3
  • 6
  • 9

💡 Hint: Recall the Product Rule.

Question 2

Is it true that if you have 15 items in 10 boxes, at least one box must contain more than one item?

  • True
  • False

💡 Hint: Think about how distribution must work.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

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.

Question 2

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.

Challenge and get performance evaluation