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

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: ind the sum of the first eight terms of the sequence 1/8,−1/4,1/2, . . ..

A:

Q: Suppose that 54% of people own dogs. If you pick two people at random, what is the that they both…

A: Given: P(Dog) = 0.54 The probability that they both own a dog can be calculated as: P(Both own a…

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

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Q: Compute the sum of the first 60 positive integers that are exactly divisible by 4.

A: The numbers divisible by 4 is:

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: List the first five terms of the sequence. a1 = 6, an+1 5an 5a,-

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Q: Find S, the sum of first 15 Natural numbers 15

A: We have to find sum of first 15 Natural numbers.   S15? Solution :  As we know that the sum of first…

Q: The sum of the first 20 terms of the sequence O.7,0.77, 0.777,.. is

A: We have to find the sum of first 20 terms of the sequence: 0.7, 0.77, 0.777, ..... Assuming the…

Q: Prove: The sum of an odd number of odd numbers must be odd.

A: Let us prove this by induction, that if n is odd and a1,a2,. . .. .an are odd, then ∑i=1nai is odd.…

Q: The greatest lower bound for the sequence {2, 4, 8, 16, 32, 64, . } is

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Q: Find at least three different sequences beginning with the terms 1, 3, 9 whose terms are generated…

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Q: The sum of the first 20 terms of the sequence 0.7, 0.77, 0.777, ... is

A: The given sequence is 0.7,0.77,0.777,...... The sum geometric sequence with common ratio r<1 ,of…

Q: Suppose that the sequence {ak}1 is 2, 4, 6, 8, 10, 12, 14, 16, . What is a,?

A: we have the given sequence 2,4,6,8,10,12,14,16,...

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

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Q: How many computer passwords of length 3 you can make out of given 5 characters a. if repetition of…

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

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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: 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: Suppose 82 jelly beans are distributed among 9 kids, with some kids possibly getting none. Fill in…

A:

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: Suppose that the sequence {ax} is =0 2, 4, 6, 8, 10, 12, 14, 16, .. What is a1?

A: The given sequence {ak}k=0∞ is -  {ak}k=0∞ = 2,4,6,8,10,12,14,16,18,......... The first tern of the…

Q: ,(n+), Does the sequences eventually increasing or decreasing ? (2n² – 7n) , (n³ – 4n²), (- , (n +…

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Q: Each customer in a certain bank has a PIN number, which is a sequence of four digits. Show that if…

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

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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: What is the 100th term of a sequence of number in which, for every positive integer x, the sum of…

A: In the given question, concept of summation series is used. Summation Series The total of the series…

Q: Registrants at a large convention are offered 6 sightseeing tours on each of 3 days. In how many…

A: Number of sightseeing tours for one day are 6. Number of days for the tour is 3.

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: How many ordered sequences are possible that contain 2  objects chosen from 9 ? ​

A:

Q: ow many bit strings have length 16? 2. How many bit strings of length 16 start with 1010? 3. How…

A: Given: A bit string is a finite sequence of 0’s and 1’s.

Q: Consider sequences of As, Bs and Cs of length 7. How many sequences have the property that the first…

A: Rule of Product (Multiplication Principle) : It is the basic counting principle . Statement  : When…

Q: Find the number of length-7 sequences from the numerical digits {0,1,2,3,4,5,6,7,8,9} such that the…

A: Combination(Selection): It refers to the situation where order of occurrence of event does not…

Q: How many sequences of n coin flips, wheren> 1/ contain no pair of consecutive heads (no HH) and no…

A: Solution

Q: How many 3-digit numbers with digits in {1,..., 9} (repeats allowed) are divisible by 9?

A: Given digits are 1,2,3,4,5,6,7,8,9. Make three digit numbers using the given digits. To find: The…

Q: How many 6-permutations of [15] have their digits in increasing order?

A: Permutation is a technique to obtain the possible arrangements of listed items in a linear order.…

Q: How many 7-letter sequences can be made using the letters in the word U R U G U A Y exactly once…

A: We have to find number of permutations possible.

Q: A Canadian postal code consists of a series of six characters of which three are letters and three…

A: There are 3 places for a letter and 3 places for a digit. There are 26 letters and 10 digits.…

Q: A coin is flipped 10 times and the sequence of heads and tails recorded. In how many ways can a…

A: Here we need to use binomial distribution

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: 35. Prove that the sequence {n!}^, beats the sequence {2"}-1-

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

A: Given number of digits in each sequence=6. Number of digits which can be used=1-9 Number of even…

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

A: To find the number of bit strings (sequences of 0's and 1's ) of length 12 and contains an equal…

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: If 40 participants are randomly selected to 4 groups of 10, does the 40 comes first in the sequence:…

A: Given: If 40 participants are randomly selected to 4 groups of 10, does the 40 comes first in the…

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: The sequence {3.1 , 3.12 , 3.123 , 3.1234 , ...} is a bounded sequence. True False

A:

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.