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

Q: 3) Sarah writes down random positive integers when she gets bored. Prove that if Sarah writes 1001…

A: Given:  Sarah writes 1001 numbers.  Since there are 10 digits, i.e., there are only 103 = 1000…

Q: How many 3 or 4 digit even numbers greater than 700 can be formed by: a. Using the digits 0-9.…

A: EVEN NUMBERS : Even numbers embrace people who conclude in zero,2,4,6, and 8. Even numbers, as an…

Q: How many eight-letter "words" (sequences of letters with repetition) are there in which vowels…

A:

Q: How many six-digit positive integers contain exactly one one, two twos and three treor? How many…

A: First note that here six digit integer can start only with 1 or 2. If it starts with 1 the remaining…

Q: How many sequences of length 5 whose elements come from the set S start with an upper case letter…

A: As per guidelines, handwritten answers are not acceptable. So, solution provided is typed. Given set…

Q: How many strings of 1our decimal digits have all four digits that are different? How many strings of…

A:

Q: How many strings of 12 ternary digits (0, 1, or 2) are there that contain exactly three 0s, five 1s,…

A: Total number of digits are 12 Given there are three 0's , five 1's and four 2's

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

A:

Q: How many strings of four decimal digits a) do not contain the same digit twice? b) end with an even…

A:

Q: Assume that you select digits from the set {1,2,3,4,5,7,8} to form a number between 10 and 800. (1)…

A: given set of digits is  {1,2,3,4,5,7,8}  and the range of numbers is 10 to 800. There would be 2…

Q: from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 if repetition is not allowed and all the odd digits occur…

A: The biggest possible number is 975,318,642; the digit zero(0) is being excluded from the question…

Q: How many numbers must be selected from the set {2,4,6,8,10,12,14,16,18,20} to guarantee that at…

A: Use the principle of inclusion and exclusion to solve this problem, as in next step.

Q: Suppose I choose two numbers from the set {1, 2, 3,... 100}. How many have an even sum? Show all…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: How many ordered sequences are possible that contain two objects chosen from nine?

A:

Q: How many numbers must be selected from the set {1, 2, 3, 4, 5, 6} to guarantee that at least one…

A: To find  How many numbers must be selected from the set {1, 2, 3, 4, 5, 6} toguarantee that at least…

Q: suppose repetitions are not allowed. Find the number n of three-digit even nimbers that can be…

A: Given problem Given that   Suppose repetitions are not allowed. Given six digits : 2,3,5,6,7,9…

Q: In one case a byte is defined as a sequence of 8 bits. Each bit can be either zero or one. How many…

A:

Q: How many different sequences of 5 ternary digits (0, 1, 2) are possible? The number of different…

A: There are total 3 choices for each digit. We will have to pick 5 digits. Each digit can be picked in…

Q: Terms of the sequence a1, a2, a3, . .. , a2020 are obtained by the rule: 1+a1 1+ a2 1+ a2019 az = 1-…

A: Reciprocal of a number n is 1n.

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

A: Here, a sequence of 120 natural numbers is given such that number n is written n times,i.e,{1, 2, 2,…

Q: Compute the sum of the first 50 positive integers that are exactly divisible by 5.

A: To determine sum of the first 50 positive integers that are exactly divisible by 5.

Q: How many ordered sequences are possible that contain fourteen objects chosen from fifteen?

A: To find the order of sequence are possible.

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

A:

Q: , n=1,2,3. is a sequence of real numbers defined by a, = /2 %3D %3D and for n21, a = 2,/2+a, .

A:

Q: A ternary digit is either 0, 1, or 2. How many sequences of nine ternary digits are possible…

A: The ternary digit is either 0 or 1 or 2.

Q: 11. What is the sum of all 4 digit numbers formed using the digits 2, 3,4 and 5 without repetition?

A:

Q: A pin number is formed by choosing an ordered sequence of 4 digits from the set {0–9} where…

A: A 4 digit pin is constructed from the set {0-9} where repetition are not allowed but numbers…

Q: How many strings of 7 decimal digits are there, such that at least one of the digit is odd?

A: There are total 10 decimal digits, among which 5 are odd. Since repetition of digits is allowed,…

Q: How many pairs of two distinct integers chosen from the set {1, 2, 3, 101} have a sum that is even?

A:

Q: In one case a byte is defined as a sequence of 8 bits. Each bit can be either zero or one. How many…

A: Permutation: A permutation of a set is defined as an arrangement of its members into a sequence or…

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

A:

Q: The total number of positive integers that can be formed from the digits 1,2,3 and 4 if no digit is…

A: Number of possible arrangement can be calculated either by combination or permutation methods.…

Q: How many 5-digit numbers can be made from the digits 1 to 9 if: a) Repetition of digits is allowed?…

A: Here AS PER POLICY I HAVE CALCULATED FIRST 3 SUBPART ONLY

Q: How many integers between 100 and 400 contain the digit 2? There are integers between 100 and 400…

A: Numbers between 200 and 299 contains 2 So total integers = 100 Numbers between 120 – 129 contains 2…

Q: set of two - digit numbers obtained from the digits 1

A:

Q: How many three-digit odd integers can be formed using the digits 0, 1, 4, 5, 6, 7, and 9 only once?

A: Permutation: A permutation of a set is defined as an arrangement of its members into a sequence or…

Q: (8) Suppose a license plate contains two letters followed by three digits with the first digit not…

A: We can find how many different licence plates can be printed (Repetition is allowed).

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

A:

Q: Suppose that the sequence {az}ı is k=1 1,3, 5, 7,9, 11, 13,.. What is a1?

A: First we find the general of the given sequence {ak}∞k=1=1,3,5,7,9,11,13,..., with the help of…

Q: A sequence a1, a2, a3,.... satisfies the property that an+1 is the average of the first n terms if…

A: We have to find a2 .

Q: itially, 10 people have an infection. The next day, every infected people infects one more person.…

A: To find the number of days it will take for 1280 people to infect.

Q: 3) Among a group of seven (not necessarily consecutive) integers, how many must be divided by 5 to…

A: This is a problem related to divination rule of the mathematics. Based on the general concept we…

Q: How many sequences of 6 positive digits (1-9) contain at least one digit that appears twice?

A: We have to determine the total sequences of 6 positive digits (1-9) that contain at least one digit…

Q: Don't copy from google or other sites  How many bit strings of length 11 contain either five…

A: Given, the strings of length 11 contain either five consecutive 0s or five consecutive 1s.

Q: A license plate is a sequence of 2 letters followed by 2 different digits.     A letter is A…

A: There are totally 26 letter and 10 digits. A license plate is a sequence of 2 letters followed by 2…

Q: How many three-digit numbers can be constructed from the digits 0, 1,2,3,4,5,6,8,9 if the number…

A: Given digits is0, 1, 2, 3, 4, 5, 6, 7, 8, 9Total no.of digits=10

Q: Assume that you are to select digits from the set {2,5,6,8,9} to form a number between 20 and 900.…

A: Assume that you are to select digits from the set {2,5,6,8,9} to form a number between 20 and 900.…

Q: how many 8-letter sequences formed from 4 letters (a,b,c,d) can occur with repetition allowed such…

A: According to the given information, it is required to find how many 8 letter sequences from 4…

Q: In a lottery game, a ticket has a total of 37 numbers to choose from, a player can mark 6 numbers on…

A: Given that, In a lottery game, a ticket has a total of 37 numbers to choose from, a player can mark…

Q: How many strings of 1our decimal digits have all four digits that are different?

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.