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4. How many 6-digit numbers (using 1,2,3, ... ,9) are there if repetition is not allowed? How many are there which have at least one digit repeated?

4. How many 6-digit numbers (using 1,2,3, ... ,9) are there if repetition is not allowed? How many are there which have at least one digit repeated?

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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How can we solve questions 4, 6, and 8 ? Using repetition, subsets, and coefficients?
allowed? Section: hy lists of length 3 can be made from the letters U, V, W, X, Y, Z if repetitions are 6x6x6 = 216 2. How many lists of length 3 can be made from the letters U, V, W, X, Y, Z if repetitions are not allowed? 6x5x4 120 3. How many lists of length 3 can be made from the letters U, V, W, X, Y, Z if repetitions are not allowed, and each list has a W or U in the second entry? 40 5. Compute the following: (a) 6! = 720 10! (b) 7! 5 хар ха X 4. How many 6-digit numbers (using 1,2,3,... ,9) are there if repetition is not allowed? How many are there which have at least one digit repeated? 10.9.2 - 10.9.8 = 120 = 720 6. How many 5-element subsets does the set {A, B, C, D, E, F, G, H, I, J} have? 7. Write the expansion of (a +6²)4. Q4+4a³b² +6a³b4+4ab64b8 8. What is the coefficient of r6 in (x+3)7? *The examples, section numbers are from Richard Hammack's "Book of Proof". *The examples, section numero e
Transcribed Image Text:allowed? Section: hy lists of length 3 can be made from the letters U, V, W, X, Y, Z if repetitions are 6x6x6 = 216 2. How many lists of length 3 can be made from the letters U, V, W, X, Y, Z if repetitions are not allowed? 6x5x4 120 3. How many lists of length 3 can be made from the letters U, V, W, X, Y, Z if repetitions are not allowed, and each list has a W or U in the second entry? 40 5. Compute the following: (a) 6! = 720 10! (b) 7! 5 хар ха X 4. How many 6-digit numbers (using 1,2,3,... ,9) are there if repetition is not allowed? How many are there which have at least one digit repeated? 10.9.2 - 10.9.8 = 120 = 720 6. How many 5-element subsets does the set {A, B, C, D, E, F, G, H, I, J} have? 7. Write the expansion of (a +6²)4. Q4+4a³b² +6a³b4+4ab64b8 8. What is the coefficient of r6 in (x+3)7? *The examples, section numbers are from Richard Hammack's "Book of Proof". *The examples, section numero e
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