1. Consider length-8 strings of digits (alphabet: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}). (a) How many are there? (b) How many end with 0? (c) How many end with two even digits? (d) How many either have only odd digits or have only even digits and end with 0? (e) How many are palindromes? (Example: 14255241) (f) How many start with an even digit or end with two even digits (or both)? (g) How many don't start with 000? (h) How many have exactly three Os? (i) How many have exactly three Os, two 1s, and three 2s? (j) How many have no digits that appear more than once? (k) How many end with four distinct even digits? (1) How many have no even digits that appear more than once? (m) How many have no digits that appear more than once, have both 0 and 1, and 0 and 1 are not adjacent? (n) How many have digits that are in increasing order? (Example: 01245679) (o) How many have digits that are in nondecreasing order? (Example: 13335788)
1. Consider length-8 strings of digits (alphabet: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}). (a) How many are there? (b) How many end with 0? (c) How many end with two even digits? (d) How many either have only odd digits or have only even digits and end with 0? (e) How many are palindromes? (Example: 14255241) (f) How many start with an even digit or end with two even digits (or both)? (g) How many don't start with 000? (h) How many have exactly three Os? (i) How many have exactly three Os, two 1s, and three 2s? (j) How many have no digits that appear more than once? (k) How many end with four distinct even digits? (1) How many have no even digits that appear more than once? (m) How many have no digits that appear more than once, have both 0 and 1, and 0 and 1 are not adjacent? (n) How many have digits that are in increasing order? (Example: 01245679) (o) How many have digits that are in nondecreasing order? (Example: 13335788)
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 54SE: How many unique ways can a string of Christmas lights be arranged from 9 red, 10 green, 6 white, and...
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Transcribed Image Text:1. Consider length-8 strings of digits (alphabet: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}).
(a) How many are there?
(b) How many end with 0?
(c) How many end with two even digits?
(d) How many either have only odd digits or have only even digits and end with 0?
(e) How many are palindromes? (Example: 14255241)
(f) How many start with an even digit or end with two even digits (or both)?
(g) How many don't start with 000?
(h) How many have exactly three Os?
(i) How many have exactly three Os, two 1s, and three 2s?
(j) How many have no digits that appear more than once?
(k) How many end with four distinct even digits?
(1) How many have no even digits that appear more than once?
(m) How many have no digits that appear more than once, have both 0 and 1, and 0 and 1
are not adjacent?
(n) How many have digits that are in increasing order? (Example: 01245679)
(o) How many have digits that are in nondecreasing order? (Example: 13335788)
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