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HW1 - CSE21 FA11 Homework#1 1.1 An n-digit number is a list...

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CSE21 FA11 Homework #1 (9/26/11) 1.1. An n -digit number is a list of n digits where the first digit in the list is not zero (where we assume n 1). (a) How many n -digit numbers are there (as a function of n )? (b) How many n -digit numbers contain no 1’s? (c) How many n -digit numbers contain at least one 2? 1.2. In how many ways can a 10-person club select a president, a vice- president and a secretary-treasurer from among its members? What if the club has 6 men and 4 women and the three officers must consist of at least one man and at least one women? 1.3. In a certain distant galaxy (far away, of course!), the alphabet contains only five symbols which we will represent as A, E, R, S, T. (A and E are called vowels, while R, S and T are consonants). All names are 5 letters long, begin and end with consonants and contain at least two vowels. Adjacent consonants must be the same, while adjacent vowels must be different. How many possible names are there?

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