A Harry Potter - Themed Quiz on Combinatorics

15 Points Per Correct Answer - No time limit  

1. In her Arithmancy class, Hermione was asked to form 5 - digit even numbers from the numbers 1, 4, 5, 8, and 0. How many can she make if repetition of numbers is not allowed? 72 60 288 36

2. Suppose Professor Mc Gonagall was making a list of possible passwords for the Gryffindor Tower. If she were to make passwords of 7 distinct letters from the letters of the English alphabet, how many of these passwords will have "A" in the middle? 127,512,000 720 167,765,600 5,040

3. In how many ways can 11 Slytherins line up outside the Divination classroom if Malfoy must be immediately between Crabbe and Goyle? 725,760 80,640 2,177,280 241,920

4. At the Yule Ball during Harry's 4th year, eight students (Hermione, Ron, Fred, George, Neville, and 3 Beauxbatons students) are seated around a table. In how many ways can they be arranged if the 3 Beauxbatons students insist on sitting next to each other and Hermione and a seemingly jealous Ron insist on sitting apart? 36 72 432 1,728

5. In Charms, Harry was asked to use a hovering charm to transfer two blue boxes, three red boxes, five brown boxes, and four yellow boxes onto a shelf. Assuming that boxes of the same color are indistinguishable, in how many ways can they be arranged on the shelf? 24 14! 2,522,520 829,440

6. Mrs. Figg invited Ron, Harry, and Hermione to dinner. If she has 10 plates, 7 spoons, 8 forks, and 6 knives, in how many ways can she set the table? 2.56 X 10^12 3,360 300,540,195 7,717,500

7. A committee of 7 members is to be formed to put up the Christmas decorations at Hogwarts. The following volunteered: 9 teachers, 7 Hufflepuff students, 4 ghosts, 6 Gryffindors, and 3 Prefects. How many possible committees can be formed by Professor Dumbledore if a committee must have only 1 Prefect, only 1 ghost, and at most 2 teachers? 123,552 1,560,780 200,772 216,216

8. A manufacturing machine in Grunnings produces 100 pieces of drills in 30 minutes. After 1 hour, the drills are divided into groups of 4 and placed in a box. If 2% of the manufactured drills are defective, in how many ways can one select a box containing 2 defective products? 4,950 114,660 119,400 4,753

9. Dudley encontered this problem in his Math test (It wouldn't be surprising if he failed the test): "What is the 7th term in the expansion of (2x-7)^12?" Find the answer to this problem. 20,871,873,784 x^5 7,529,536 x^6 105,413,504 x^6 6,957,291,264 x^6

10. Hermione decided to make codewords for the DA that are composed of 2 letters, and 4 numbers. How many codewords are possible if the letters are taken from the English alphabet and the numbers from 0-9, and repetition is allowed? 67,600,000 49,140,000 101,400,000 4,914,000