Discrete Structures Assignment 3 1. How many different-looking arrangements are there of the letters in the word DEED? 2. How many different-looking arrangements are there of the letters in the word PUZZLE? 3. How many binary sequences are there of length 4? Of these, how many end with a 1? 4. How many binary sequences are there of length 4 use exactly two 1's and two 0's? 5. Using only the digits 1, 2, 3, 4, 5, and 6, how many five-digit numbers can be formed? How many of them have either no 5 or no 6? 6. How many positive integer solutions are there to x+y+z = 20? 7. How many nonnegative integer solutions are there to x+y+z = 20? 8. How many ways are there to distribute 200 apples among 43 women and 47 men if each woman must get at least two apples and each man must get at least one apple? 9. How many two-element subsets of {1, 2, ..., 19} are there? 10. The 9 men and 12 women in the Math Club need to form a fundraising committee. (a) How many possible committees of four people can be formed? (b) How many of these four-person committees have the same number of women as men? (c) How many of these four-person committees have more women than men? 11. What is the coefficient of x6 in the expansion of (1+x2)10? 12. A ternary sequence is a sequence of digits chosen from {0, 1, 2}. How many ternary sequences of length 12 satisfy each listed condition? (a) Exactly eleven 1's. (b) Exactly three 1's and two 0's. (c) No 1's