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
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.6: Counting Principles
Problem 8ECP: In how many different ways can two letters be chosen from the letters A, B, C, D, E, F, and G? (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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