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8. How many ways are there to arrange 12 identical apples and five different oranges in a row so that no two oranges will appear side by side? 9. (a) How many arrangements of the letters in COMBINATORICS have no con- secutive vowels? (b) In how many of the arrangements in part (a) do the vowels appear in alpha- betical order? 10. How many ways are there to arrange the 26 letters of the alphabet so that no pair of vowels appear consecutively (Y is considered a consonant)? 11. If you flip a coin 18 times and get 14 heads and four tails, what is the probability that there is no pair of consecutive tails?. 12. How many integer solutions are there to x₁ + x2 + x3+x+x5=31 with (a) x; ≥ 0 (b) x; > 0 (c) x ≥i(i=1,2,3,4,5) 13. How many integer solutions are there to x₁ + x2 + x3 =0 with x ≥-52 14. How many positive integer solutions are there to x1 + x₂+x+x<50? 15. How many ways can a deck of 52 cards be broken up into a collection of unordered piles of sizes (a) Four piles of 13 c. rds? (b) Three piles of eight cards and four piles of seven cards? 22 division

8. How many ways are there to arrange 12 identical apples and five different oranges in a row so that no two oranges will appear side by side? 9. (a) How many arrangements of the letters in COMBINATORICS have no con- secutive vowels? (b) In how many of the arrangements in part (a) do the vowels appear in alpha- betical order? 10. How many ways are there to arrange the 26 letters of the alphabet so that no pair of vowels appear consecutively (Y is considered a consonant)? 11. If you flip a coin 18 times and get 14 heads and four tails, what is the probability that there is no pair of consecutive tails?. 12. How many integer solutions are there to x₁ + x2 + x3+x+x5=31 with (a) x; ≥ 0 (b) x; > 0 (c) x ≥i(i=1,2,3,4,5) 13. How many integer solutions are there to x₁ + x2 + x3 =0 with x ≥-52 14. How many positive integer solutions are there to x1 + x₂+x+x<50? 15. How many ways can a deck of 52 cards be broken up into a collection of unordered piles of sizes (a) Four piles of 13 c. rds? (b) Three piles of eight cards and four piles of seven cards? 22 division

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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8. How many ways are there to arrange 12 identical apples and five different oranges in a row so that no two oranges will appear side by side? 9./ (a) How many arrangements of the letters in COMBINATORICS have no con- secutive vowels? (b) In how many of the arrangements in part (a) do the vowels appear in alpha- betical order? 10. How many ways are there to arrange the 26 letters of the alphabet so that no pair of vowels appear consecutively (Y is considered a consonant)? 11. If you flip a coin 18 times and get 14 heads and four tails, what is the probability that there is no pair of consecutive tails? 12. How many integer solutions are there to x+x2+x3+X4+xs 31 with (e) x즈 i(i =D 1, 2.3.4,5) (a) x; 20 (b) x; > 0 13. How many integer solutions are there to x +x2+X33D0 with x; 2-52 14. How many positive integer solutions are there to x, +x++x <50? 15. How many ways can a deck of 2 cards be broken up into a collection of unordered piles of sizes (a) Four piles of 13 c. rds? (b) Three piles of eight cards and four piles of seven cards? 23 division e
Transcribed Image Text:8. How many ways are there to arrange 12 identical apples and five different oranges in a row so that no two oranges will appear side by side? 9./ (a) How many arrangements of the letters in COMBINATORICS have no con- secutive vowels? (b) In how many of the arrangements in part (a) do the vowels appear in alpha- betical order? 10. How many ways are there to arrange the 26 letters of the alphabet so that no pair of vowels appear consecutively (Y is considered a consonant)? 11. If you flip a coin 18 times and get 14 heads and four tails, what is the probability that there is no pair of consecutive tails? 12. How many integer solutions are there to x+x2+x3+X4+xs 31 with (e) x즈 i(i =D 1, 2.3.4,5) (a) x; 20 (b) x; > 0 13. How many integer solutions are there to x +x2+X33D0 with x; 2-52 14. How many positive integer solutions are there to x, +x++x <50? 15. How many ways can a deck of 2 cards be broken up into a collection of unordered piles of sizes (a) Four piles of 13 c. rds? (b) Three piles of eight cards and four piles of seven cards? 23 division e
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