A decimal string is a string over the alphabet of the 10 characters: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. How many decimal strings of length 6 are there that consist of 6 different characters in decreasing order? How many decimal strings of length 6 are there that have at least one letter OR at least one 0?

Q: How many bits string of length 4 are possible such that they contain 2 ones and 2 zeroes?

A: 2. Given Data: The length of string is: n=4 The number of ones is: 2 The number of zeros is: 2   The…

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Q: How many 8-bit strings of weight 5 start with 101 or end with 10 or both?

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Q: A bit string is a finite sequence of O's and 1's. How many bit strings of length 9 begin with 10 and…

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Q: Find all three-digit numbers with different digits with the property that those numbers are…

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Q: A sequence of  120 natural numbers is given such that number n is written n times…

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Q: ive distinct integers are to be chosen from the set {1,2,3,4,5,6,7,8} and placed in some order in…

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Q: How many bit strings of length 10 contain at least three 1s and three

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Q: A ternary bit string is a string of digits from {0, 1, 2}. How ternary bit strings are there of…

A: Solution of the problem as follows

Q: (a) Show that if seven integers are selected from the first 10 positive integers, there must be at…

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Q: Use generating functions to determine the number of differentways 15 identical stuffed animals can…

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Q: How many 10-bit strings are there if the string must start with 001 or 10?

A: By using the given information the solution is given as follows

Q: ,1), (2, 2), (1, 3), (4, 1), (3, 2), (2, 3), (1,4), (5, 1), .... Show that this constitutes a proof…

A: We will answer the first question only as we don't answer multiple questions at a time. Please…

Q: (a) that the gap between the largest integer and the second largest one is at least 3. Show all…

A: Solution: Given The number of ways to select six integers from 1,2,..., n such that the gap between…

Q: How many 10-bit strings are there if the string must have exactly one 1 in the first half and…

A: The string must contain exactly one 1 in the first half and exactly one 1 in the second half. So…

Q: 4. Suppose that Mr. H paid $500 for his insurance in 2018. It is expected that every year the…

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Q: How many bit strings of length n, where n is a positive integer, start and end with 1s

A: First place 1 at the start and end of the n bit string. Then there are n-2 bit strings.

Q: How many positive integers less than 10000 are there which contain at least one 2 or at least one 3…

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Q: A bit string is a finite sequence of O's and l's. How many bit strings have length 9? bit strings…

A: The number of bit strings in each case are found as shown below.

Q: A sequence of 120 natural numbers is given such that number n is written n times {1, 2, 2, 3, 3, 3,…

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Q: The sum of all positive integers less than 300 which are not divisible by 3.

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Q: The set of numbers whose decimal representations are neither terminating numbers. repeating is…

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Q: How many strings of ten lowercase letters from the English alphabet contain the lette consecutive…

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Q: Determine the number of strings of length 10 from the alphabet {A, B, C} that contain exactly 3 A's…

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Q: How many combinations are there to pick r objects from 2n objects numbered from 1 to 2n with n > 2…

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Q: Find the number of permutations x1, x2, x3, x4, x5,  of numbers 1, 2, 3, 4, 5 such that the sum of…

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Q: Suppose a password for a computer system must have at least 7, but no more than 11 characters where…

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Q: Five distinct integers are to be chosen from the set {1, 2, 3, 4, 5, 6, 7, 8} and placed in some…

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Q: A product code consists of a string of 4 different letters selected from the set {S,T,U,V,W,X}. How…

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Q: Use generating functions to determine the number of differentways 10 identical balloons can be given…

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Q: How many three digit passcode can be made from the digits 0-9in the first number is not allowed to…

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Q: Use generating functions to find the number of ways tochoose a dozen bagels from three…

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Q: How many strings of length 6 decimal digits are there such that the first digit or the last digit is…

A: Since you have asked multiple questions here, we will solve the first question for you. To get the…

Q: ) How many,8-distinct/digit numbers can be formed if the numbers áre amultiple of/5 and contain the…

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Q: 5 can be formed if the alphabet (set of avail

A: To find: Number of strings of length 5 that can be formed with {a,b,c} with last character not as b.

Q: A string that contains only Os, 1s, and 2s is called a ternary string. How many ternary strings of…

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Q: How many strings are there of length 6 over the alphabet {a, b, c, A, B} in which exactly two of the…

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Q: How many bit strings of length 10 contain either five con- secutive Os or five consecutive 1s? How…

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Q: How many sequences of 6 positive digits (1-9) contain at most one even digits?

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Q: how many bit strings (sequences of 0's and 1's) of length 12 and contain an equal number of 0's and…

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Q: We are making 5-letter words from the set of letters a, b, c, d, e, f..., in such a way that we have…

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Q: 1. How many bit strings(strings of 1 or 0) of length 10 are there such that it contains exactly 5…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: How many bit strings of length greater than equal to one and less than or equal to six are there?

A: There are 2 possible bits : 0 and 1 Bit strings of length 6 are, 2.2.2.2.2.2=26=64 Bit strings of…