Sample Exam Questions for Exam II
  1. Prove (by induction) that for all n >= 1, a set with n elements has n(n - 1)(n - 2) / 6 subsets of size 3.  You may use the fact that a set with n elements has n(n - 1) / 2 subsets of size 2.
  2. Prove (by induction) that for all n >= 1, 1*2 + 2*3 + 3*4 + ... + n(n + 1) = n(n+1)(n+2) / 3
  3. How many 4-digit numbers are there with no repeated digits?
  4. How many 5-digit numbers are there with no repeated even digits?  (Odd digits may be repeated.)
  5. How many anagrams are there of the word "FLUFF" which have no two F's next to each other?
  6. How many anagrams are there of the word "BLUFF" which have no two F's next to each other?
  7. How many anagrams are there of the word "AABBCDEFG" which have the A's apart from each other and the B's apart from each other?
  8. How many ways are there to put 4 quarters into 10 pockets?
  9. How many ways are there to put 15 quarters into 5 pockets so that the ith pocket gets at least i quarters, for i = 1, 2, 3, 4, 5?
  10. How many ways are there to put 18 quarters into 5 pockets so that the ith pocket gets at least i quarters, for i = 1, 2, 3, 4, 5?
  11. What is the sum 2 + 5 + 8 + 11 + ... + 98?
  12. What is the sum 2 + 6 + 18 + 54 + ... + 2*315?
  13. Evaluate
  14. Evaluate
  15. Draw the first 10 rows of Pascal's Triangle.
  16. What is the sum 1 + 3 + 6 + 10 + 15 + ... + 5050, that is, the sum of the "Choose 2" numbers from rows 2 through 101 of Pascal's Triangle?
  17. Wanda has 30 distinct white rocks.  She selects some (0 - 30) of them to paint red, and then she selects some of the ones she painted red and paints smiley faces on them.  In how many ways can this be done?
In addition, make sure you can do the homework problems that have been assigned (including the one due the day of the test) and also the quizzes which have been given.