Clicker Questions - 09-Enumeration
Please make your answers mathematical expressions involving exponents and factorials. I’d prefer that you not simplify them or multiply them out.
The number in answers is how many students got this right when it was given on the 2017 midterm.
Question 1: I am a salesman whose route covers 12 cities. In how many different orders can I visit all 12 cities, if I’m not allowed to visit a city twice?
Answer
(92.2%) The answer is the number of permutations of the cities: 12!Question 2: On the planet vowelopia, everyone’s name has to contain exactly 10 characters, which can only be vowels (A, E, I, O, U). How many distinct names are there?
Answer
(68.8%) The number of 10-character strings from a 5-character alphabet: $5^{10}$.Question 3: My basketball team has 12 players. At any one time, there can only be 5 players on the court. How many different combinations of players can there be on the court?
Answer
My basketball team has 12 players. At any one time, there can only be 5 players on the court. How many different combinations of players can there be on the court?Question 4: How many subsets are there of the set $\{ 34, 52, 22, 66, 43, 1 \}$
Answer
(48.1%) That's a power set enumeration: $2^{6}$.Question 5: If I have 15 different colored balls, how many ways are there to put them into 15 numbered boxes?
Answer
(66.2%) This is the number permutations of the 15 balls: 15!Question 6: If I have 5 identical white balls and 18 identical black balls, how many ways are there to put them into 23 numbered boxes?