Practice Combined Use Of Sum And Product Rule (10.4) - Basic Rules of Counting

Practice: Combined Use of Sum and Product Rule

Lesson 10.4Basic Rules of Counting

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8 questions

Flashcard drill
3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
How many ways can 3 students be chosen from a set of 5?
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Use C(n, k) = n! / (k!(n-k)!), where n is the total number and k is the number of choices.
Question 2.
If each student can pick one of 4 different books, how many choices are there for 3 students?
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Use the Product Rule: 4^3.
3Question 3.
How many ways can 2 employees be assigned to 3 different offices if they cannot share an office?
- 3
- 6
- 9
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Recall the Product Rule.
4Question 4.
Is it true that if you have 15 items in 10 boxes, at least one box must contain more than one item?
- True
- False
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Think about how distribution must work.
Question 5.
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.
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Visualize relationships as graphs.
Question 6.
For valid passwords of lengths 6, 7, and 8 using specified character sets, solve for total valid combinations accounting for at least one digit.
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Group by length for efficient counting.

4 more questions in this section. Enroll free to practise them all.