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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?

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.1: Counting
Problem 92E: DISCUSS: Complementary Combinations Without performing any calculations, explain in words Why the...
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How can we find out how many 6 digit numbers are there if not allowed and how many 5 element subsets does a,b,c,d,e,f,g,h,i,j have?
1. How many lists of length 3 can be made from the letters U, V, W, X, Y, Z if repetitions are allowed? 6x6 x 6 = 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? 5 хоха 40 5. Compute the following: (a) 6! 720 Section: 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? - 10-9:1:21 10! (b) 7! (c) (12) 6. How many 5-element subsets does the set {A, B, C, D, E, F, G, H, I, J} have? 10.9.8 = 120 = 720 7. Write the expansion of (a + b²)4. 94 +4a³b² +6ab4+4ab6+b8 8. What is the coefficient of r6 in (x+3)7? *The examples, section numbers are from Richard Hammack's "Book of Proof".
Transcribed Image Text:1. How many lists of length 3 can be made from the letters U, V, W, X, Y, Z if repetitions are allowed? 6x6 x 6 = 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? 5 хоха 40 5. Compute the following: (a) 6! 720 Section: 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? - 10-9:1:21 10! (b) 7! (c) (12) 6. How many 5-element subsets does the set {A, B, C, D, E, F, G, H, I, J} have? 10.9.8 = 120 = 720 7. Write the expansion of (a + b²)4. 94 +4a³b² +6ab4+4ab6+b8 8. What is the coefficient of r6 in (x+3)7? *The examples, section numbers are from Richard Hammack's "Book of Proof".
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