Purpose: Confirm prerequisite skills before working with permutations: counting principle, basic combinatorial reasoning, fraction simplification with factorials.
Prerequisite Knowledge from Ch 1 and MCR3U
Question 1 [2 marks]
A pizza has 3 crust options, 2 sauce choices, and 5 toppings. If you choose 1 crust, 1 sauce, and 1 topping, how many pizzas are possible? Explain which counting principle you used.
0 words
Question 2 [3 marks]
Evaluate without a calculator (show steps):
a) \( 5! \) b) \( \dfrac{7!}{5!} \) c) \( \dfrac{(n+1)!}{n!} \) for general \( n \)
0 words
Question 3 [2 marks]
In how many ways can a class of 4 students line up to enter a room?
0 words
Question 4 [3 marks]
A 3-digit number is formed using digits 1, 2, 3, 4, 5 without repetition.
a) How many such numbers are possible?
b) How many are odd?
0 words
Question 5 [3 marks]
Solve algebraically: \( \dfrac{n!}{(n-2)!} = 12 \). Find all valid \( n \in \mathbb{N} \).
0 words
Question 6 [3 marks]
Reflection: What is the difference between an "ordered" arrangement and an "unordered" selection? Give an example of each from your daily life.