Homework Assignment Seven

  1. How many different license plates involving 3 letters and 3 digits are there if the three letters appear at the beginning or at the end of the license plate?
  2. What is the probability that the sum of two randomly chosen integers from the range 20-40 (inclusive) is even? Note: it's possible that the two chosen numbers are identical.
  3. How many times is the digit 5 written when listing all of the numbers from 1 to 100,000.
  4. How many non-empty collections can be formed from a set of n A's, n B's, n C's, and n D's?
  5. How many distinct arrangements are there of the letters in the the word "DRIVING"?
  6. How many ways are there to choose 6 different letters from the 26-letter alphabet?
  7. If 13 players are each dealt 4 cards from a 52 card deck, what is the probability that each player gets one card from each suit?
  8. How many ways are there to pair off 10 women at a dance with 10 out of 20 available men?
  9. How many arrangements are there of the letters in the word "JUPITER" with the restriction that the vowels appear in alphabetical order?
  10. How many arrangements of five 0's and ten 1's are there with no pair of consecutive 0s?
  11. How many arrangements of the integers 1, 2, ..., n are there such that each integer differs by 1 (except for the first integer) from some integer to the left of it in the arrangement?
  12. How many ways are there to arrange the letters in the word MISSISSIPPI?
  13. How many arrangements of the letters in the word TINKERER are there, with the restriction that there must be 2 but not 3 consecutive vowels?
  14. How many ways are there to distribute 7 (indentical) apples, 6 oranges, and 7 pears among 3 different people: a) without restriction; and b) with each person getting at least one pear?
  15. How many positive integer solutions are there to the equation (x+y+z+w) < 100?
  16. Show that (n!)**(n+1) evenly divides (n**2)! [Recall that x**y means "x raised to the power y"]
Collaboration acceptable on #7, 11, 15, 16

Due: Thursday October 23, in class

-- RobbieMoll - 25 Mar 2009

Topic revision: r8 - 2014-10-16 - RobbieMoll
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