Homework Assignment Nine

You may collaborate on numbers 4,5, 8. Notation in brackets are references to problems in Tucker, 5th edition.

  1. Find the coefficient of x18 in (1+x3+x6+x9+...)7[6.2.14]
  2. In the US there are 50 states, each with 2 senators. How many different committees of 40 senators can be formed if the two senators from the same state are considered to be identical? [6.2.24]
  3. How many ways are there to divide 5 pears, 5 apples, 5 doughnuts, 5 lollipops, 5 chocolate cats, and 5 candy rocks into two (unordered) piles of 15 objects each? [6.2.26]
  4. How many r-digit ternary sequences are there in which a) no digit occurs exactly twice; and b) 0 and 1 each occurs an even number of times. [6.4.10]
  5. Find a recurrence relation for the number of ways to go N miles by foot walking at 3 mph, or jogging 5 mph, or running 10 mph; at the end of each hour a choice is made about how to go during the next hour. [7.1.4]
  6. Find a recurrence relation for the number of n-digit binary sequences with a) no pair of consecutive 1s; b) no pair of consecutive 1s, but for ternary sequences; and c) no pair of consecutive 0s and 1s, for ternary sequences. [7.1.6]
  7. Show that sN = C(N+1,0)+ C(N,1) + C(N-1, 2)... satisfies the Fibonacci relation.[7.1.8]
  8. Find and solve a recurrence for the number of n-digit ternary sequences with no consecutive digits being equal. [7.3.2]
Due: Wednesday November 12

-- RobbieMoll - 08 April 2009

Topic revision: r4 - 2014-12-08 - RobbieMoll
 
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