Purpose: Confirm prerequisite skills before working with combinations: factorials, permutations from Ch 2, basic algebra (solving quadratic equations).
Prerequisite Knowledge from Ch 1, Ch 2 and MCR3U
Question 1 [3 marks]
Evaluate without a calculator (show steps):
a) \( \dfrac{10!}{8!\,2!} \) b) \( \dfrac{n(n-1)(n-2)}{3!} \) for \( n=5 \) c) \( P(7,3) \)
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Question 2 [2 marks]
Decide whether each scenario involves a permutation (order matters) or a combination (order does not matter):
a) Selecting a 4-person committee from a club of 10.
b) Awarding gold, silver, and bronze in an 8-person race.
c) Choosing 3 books to take on a trip from 7 books.
d) Arranging 5 books on a shelf.
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Question 3 [3 marks]
Solve the quadratic equations (use the quadratic formula or factoring):
a) \( n^2 - 5n - 14 = 0 \)
b) \( n(n-1) = 30 \)
c) \( n^2 + 3n - 28 = 0 \)
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Question 4 [2 marks]
Construct the first 5 rows of Pascal's triangle (rows 0 through 4). Then state the sum of the entries in row 4.
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Question 5 [2 marks]
Expand \( (x+y)^3 \) using FOIL or by multiplying \( (x+y)(x+y)(x+y) \). Show all steps.
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Question 6 [3 marks]
Reflection: After Ch 2, what do you find most confusing about deciding whether a problem is a permutation or a combination? Describe a specific scenario you struggled with.