# Homework Assignment Ten

You may collaborate on numbers 1,3,5,7.

1. Find a recurrence for the number of n-letter sequences using letters A, B, and C, such that any A not in final position in the sequence is always followed by a B. [7.1.18]
2. Find a recurrence for the number of n-digit binary sequences with at least one instance of consecutive 0's.[7.1.22]
3. Find a recurrence for the number of ways to arrange three types of flags on a flagpole n feet high, red flags (1 foot high), gold flags (1 foot high), and green flags (2 feet high), with the added condition that there cannot be 3 one foot flags in a row [7.1.20]
4. Solve the recurrence an = 3an-1 + n2 - 3, with a0 = 1. [7.4.10]
5. Find and solve a recurrence for the number of n-digit ternary sequences in which no 1 appears (anywhere) to the right of any 2 - so these are bad sequences: 21, 20001, 222220000001. [7.4.12]
6. How many arrangements of the 26 different letters of the alphabet are there that contain either the sequence "the" or the sequence "aid"?[8.1.12]
7. How many 4 digit numbers (including leading 0s) with no digit occuring exactly 2 times? [8.2.12]
8. How many arrangments of 1,2,...,n are there in which only the odd integers are deranged (even integers may be in their own original positions)? [8.2.18]
Due date - in class, November 20

-- RobbieMoll - 17 Apr 2009

Topic revision: r9 - 2014-11-19 - RobbieMoll

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