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Unformatted text preview: 201001 Math 222 Sample Final Exam 1. Let S 1 and S 2 be sequences of 7 decimal digits. Suppose we say that S 1 is equivalent to S 2 if S 1 is a rearrangement of S 2 . For example 1231236 is equivalent to 2263311. (a) How many sequences are equivalent to 9955500? (b) What is the maximum possible size of a set of sequences, no two of which are equivalent? 2. Give a combinatorial argument to show that 2 n 2 ! = 2 n 2 ! + n 2 . 3. Prove that no matter how 51 different integers are selected from { 1 , 2 ,..., 100 } the selections contains a and b such that b is a multiple of a . 4. How many ways are there to place 8 rings on the 4 fingers of your left hand if: (a) The rings are identical. (b) The rings are identical and at least one ring must be put on each finger. (c) The rings are different and the order of rings on a finger is not important. (d) The rings are different and the order of rings on a finger is important....
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This note was uploaded on 01/15/2012 for the course MATH 222 taught by Professor Huangjing during the Spring '11 term at University of Victoria.
 Spring '11
 HuangJing
 Math

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