6.5 Worksheet Exercise 6.5.3: Counting bit strings. How many 10-bit strings are there subject to each of the following restrictions? (a) No restrictions. 2. (b) The string starts with 001. (c) The string starts with 001 or 10. (d) The first two bits are the same as the last two bits. 6. (e) The string has exactly six O's. to ta Cl0, 6)dmon bne eousums 2a salbaxa (f) The string has exactly six O's and the first bit is 1. (g) There is exactly one 1 in the first half and exactly three 1's in the second half. (5,3) Exercise 6.5.4: Counting strings of letters. woh How many different strings of length 12 containing exactly five a's can be chosen over the following alphabets? (a) The alphabet {a, b} ך1 (1'ב (b) The alphabet {a, b, c} (Lכ(ו Page 2 of 4 Exercise 6.5.1: Mapping permutations to subsets. e Consider a function f that maps 5-permutations from the set S = (1, ..., 20} to 5-subsets from S. The function takes a 5-permutation and creates an unordered set whose elements are the five numbers included in the 6.5 Worksheet permutation. (a) What is the value of f on input (12, 1, 3, 15, 9)? (b) Is (12, 3, 12, 4, 19) a 5-permutation? Why or why not?. e 6.7.1: Cour Yes because ny different pas then wons? Parens gth is 6 and the tockes (c) How many permutations are mapped onto the subset {12, 3, 13, 4, 19}? Pand Length is 67 Exercise 6.5.2: Permutations and combinations from a set of letters. Define the set S = {a, b, c, d, e, f, g}. (a) Give an example of a 4-permutation from the set S. is 5. %3D (Pis'qio) (b) Give an example of a 4-subset from the set S. Exer A 5-r () e0nd vhasxo bne tori tot orb mlgnoyoGxo eloedT {pigialin} Halto (c) How many subsets of S have exactly four elements? inicio onie e exsced Com EXGL ih (d) How many subsets of S have either three or four elements? (p)19buspe p ck iL 3. Page 1 of 4
6.5 Worksheet Exercise 6.5.3: Counting bit strings. How many 10-bit strings are there subject to each of the following restrictions? (a) No restrictions. 2. (b) The string starts with 001. (c) The string starts with 001 or 10. (d) The first two bits are the same as the last two bits. 6. (e) The string has exactly six O's. to ta Cl0, 6)dmon bne eousums 2a salbaxa (f) The string has exactly six O's and the first bit is 1. (g) There is exactly one 1 in the first half and exactly three 1's in the second half. (5,3) Exercise 6.5.4: Counting strings of letters. woh How many different strings of length 12 containing exactly five a's can be chosen over the following alphabets? (a) The alphabet {a, b} ך1 (1'ב (b) The alphabet {a, b, c} (Lכ(ו Page 2 of 4 Exercise 6.5.1: Mapping permutations to subsets. e Consider a function f that maps 5-permutations from the set S = (1, ..., 20} to 5-subsets from S. The function takes a 5-permutation and creates an unordered set whose elements are the five numbers included in the 6.5 Worksheet permutation. (a) What is the value of f on input (12, 1, 3, 15, 9)? (b) Is (12, 3, 12, 4, 19) a 5-permutation? Why or why not?. e 6.7.1: Cour Yes because ny different pas then wons? Parens gth is 6 and the tockes (c) How many permutations are mapped onto the subset {12, 3, 13, 4, 19}? Pand Length is 67 Exercise 6.5.2: Permutations and combinations from a set of letters. Define the set S = {a, b, c, d, e, f, g}. (a) Give an example of a 4-permutation from the set S. is 5. %3D (Pis'qio) (b) Give an example of a 4-subset from the set S. Exer A 5-r () e0nd vhasxo bne tori tot orb mlgnoyoGxo eloedT {pigialin} Halto (c) How many subsets of S have exactly four elements? inicio onie e exsced Com EXGL ih (d) How many subsets of S have either three or four elements? (p)19buspe p ck iL 3. Page 1 of 4
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:6.5 Worksheet
Exercise 6.5.3: Counting bit strings.
How many 10-bit strings are there subject to each of the following restrictions?
(a) No restrictions.
2.
(b) The string starts with 001.
(c) The string starts with 001 or 10.
(d) The first two bits are the same as the last two bits.
6.
(e) The string has exactly six O's.
to ta Cl0, 6)dmon bne eousums 2a salbaxa
(f) The string has exactly six O's and the first bit is 1.
(g) There is exactly one 1 in the first half and exactly three 1's in the second half.
(5,3)
Exercise 6.5.4: Counting strings of letters.
woh
How many different strings of length 12 containing exactly five a's can be chosen over the following
alphabets?
(a) The alphabet {a, b}
ך1 (1'ב
(b) The alphabet {a, b, c}
(Lכ(ו
Page 2 of 4
Transcribed Image Text:Exercise 6.5.1: Mapping permutations to subsets. e
Consider a function f that maps 5-permutations from the set S = (1, ..., 20} to 5-subsets from S. The function
takes a 5-permutation and creates an unordered set whose elements are the five numbers included in the
6.5 Worksheet
permutation.
(a) What is the value of f on input (12, 1, 3, 15, 9)?
(b) Is (12, 3, 12, 4, 19) a 5-permutation? Why or why not?.
e 6.7.1: Cour
Yes
because
ny different pas
then
wons?
Parens
gth is 6 and the
tockes
(c) How many permutations are mapped onto the subset {12, 3, 13, 4, 19}?
Pand
Length is 67
Exercise 6.5.2: Permutations and combinations from a set of letters.
Define the set S = {a, b, c, d, e, f, g}.
(a) Give an example of a 4-permutation from the set S.
is
5.
%3D
(Pis'qio)
(b) Give an example of a 4-subset from the set S.
Exer
A 5-r
()
e0nd vhasxo bne tori tot orb mlgnoyoGxo eloedT
{pigialin}
Halto
(c) How many subsets of S have exactly four elements? inicio onie e
exsced
Com
EXGL
ih
(d) How many subsets of S have either three or four elements?
(p)19buspe p ck
iL
3.
Page 1 of 4
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