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EXERCISES 5.1 (Page 185) 5.2 (Page 198) PROBLEMS 9,10,13,15, 18, 20, 22,23, 26-29 7-12, 14, 20-26, 32, 33, 36-58 1. How many different integers between 1000 and 10000 are there with (a) distinct digits 9×9×8×7 (b) repetition of digits allowed but with no 2 or 4 7×8×8×8+1 (c) distinct digits and at least one of 2 and 4 must appear (9 × 9x8x7)-(7x7x6x5) 2. What is the probability that a number between 1 and 10,000 has exactly one 8 and one 9? 3. Given 8 different English books, seven different French books and five different German books how many ways are to make a row of three books in which exactly one language is missing? 4. How many n-digit ternary sequences with exactly 9 zeros are there? n-9 9 5. How many ternary sequences of length 10 are there without any pair of consecutive digits the sane 9 6. What is the probability of randomly choosing choosing a permutation of the 10 digits, 0,1...9, in which (a) An odd digit is in the first position and 1,2,3,4, or 5 is in the last position? 10! (b) 5 is not in the first position and 9 is not in the last position? 10! 7. How many nonempty collections of letters can be formed from 3 As and 5 Bs? 8. How many arrangements of INSTRUCTOR are there in which there are exactly two consonants between successive pair of vowels? 1.О.U, N.S2.T.C2.R 4×31×() × G) × 3! 9. How many different 5-letter sequences can be made using the letters A B.C.D with repetition such that the sequence does not include the word BAD? 45 3 x4 10. What fraction of all arrangements of the letters of INSTRUCTOR have (a) Three consecutive vowels? IUO, C,N,S,2.T,2.R

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