How many integers n where 1≤n≤1600 satisfy the condition ⌊n⌋\n.

Q: 3. How many 4-digit positive integers are there that are even or contain no O's?

A:

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: For what values of nn will the number of ways of selecting nn items from 60 exceed the number of…

A:

Q: Whenever n is a pOsitiv integer (n > 1). (15 points) %3D

A: Follow the procedure given below.

Q: the number of permutations of 10 distinct objects taken six at a time is 151? a. b. True False

A:

Q: Suppose that you have 19 balls to place into four different bins. Nine of the balls are red, while…

A: Given data: The total numbers of balls are n=19. The numbers of red balls are r=9. The numbers of…

Q: If the first three Fibonacci numbers are given as x, = 1, X2 = 1 and x3 = 2, then what is the least…

A: This is a question of number theory therefore from the subtopic of counting.

Q: Suppose you are at a party with 19 of your closest friends (so including you, there are 20 people…

A:

Q: How many possible results are there that A finished the first, B finished the second, and C finished…

A: SIX STUDENTS ARE SELECTED TO RUN 100 METER SPRINT. ASSUME THAT THEY ARE EQUALLY GOOD AND RESULT ARE…

Q: Ex: An experimenter partitions a field into 64 same lots. Experimenter uses 5 different seeds, 3…

A: Given, No of Lots = 64 no of seeds = 5 no of pesticides = 3  no of fertilizers = 4

Q: How many permutations π of [10] satisfy π^5 = 1?

A: The given set is 10=1,2,3,…,10. Therefore any permutation π of 10, is bijective function from the…

Q: 8. How many positive integers less than 1000 a) have exactly three decimal digits? b) have an odd…

A: According to our guideliness we can answer only the first 3 subparts. Positive integers less than…

Q: A perfect coin is tossed 1000 times in sets of 12. (1) In how many cases should we expect to get 8…

A:

Q: Assume n and m are two integers such that n > m > 1. If a bit string of length n+m is randomly…

A:

Q: XI In a group of 11 boys and 9 girls, 5 are to be selected. In how many ways can they be selected…

A: According to the answering guidelines, we can answer only one question at a time and the rest can be…

Q: how many combinations are possible? assume the items are distinct. 16 items chosen 16 at a time

A: Only one combination is possible.

Q: Suppose a set of 8 numbers are selected from the set: {1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13;…

A: It is given that 8 numbers are selected from the set 1,2,3,4,5,6,7,8,9,10,11,12,13,14.

Q: 9. This question is a little more challenging. How many integers in the interval [1, 99 999] (i.e.,…

A: Given data:   The given sum of all digits is k=10. The number of digits that can be used is n=5.…

Q: Consider a list of randomly generated 2-letter "words" printed on a paper. The letters cannot be…

A: Total number of different 2 letter word without repeated words is 26×25=650.(a)At least how many of…

Q: e) True or False: If 25 oranges are placed into 22 baskets, then at least one basket must contain at…

A:

Q: Show that for all n:  ceil(n) = -floor(-n)

A: In the given question we have to prove that ceil(n)=-floor(-n) That is…

Q: [G] Students (including yourself) from 5 area colleges are at a math conference (there are more than…

A: There are 5 colleges and I want to meet at least 8 from the same college.  Let us think of a case…

Q: How many ways are there to invite one of four different friends over for dinner on five successive…

A: Let x, y ,z, u be the friends and a, b, c, d denotes the number of times a friend is invited…

Q: Assume that you are assigning one of 12 available lockers to each of the 8 players on the team. In…

A:

Q: AMong the seven nominees for two VaGancies on the city council are three Men and four women. In how…

A:

Q: 22. It is known that a test in a class consists of 50 exam questions. If there areat least 2…

A: HERE  GIVEN THAT A TEST IN CLASS CONSIST OF 50 EXAM QUESTIONS  AND AT LEAST 2 STUDENTS WHO RECEIVE…

Q: We need to attempt to find an exact value of n such that  P(r ≥ 6) = 0.98. Clearly to guarantee…

A: We have to fill blanks from given statement Clearly to guarantee at least six people are literate,…

Q: 3. How many ways are there to distribute n identical balls in k distinguishable (labelled) boxes…

A: It is given that there are n identical balls in k distinguishable boxes.

Q: Write “the set of all natural numbers N less than 9” intwo different ways.

A: To write “the set of all natural numbers N less than 9” in two different ways.

Q: Suppose that in a certain state, all automobile license plates have three uppercase letters followed…

A: There are 26 letters [A-Z] and 10 digits [0-9] d) If the letters and digits are distinct then we can…

Q: Let S be the set of all (nonnegative) 4-digit integers. How many integers does S contain?

A:

Q: How many times would you expect to roll a fair die before all 6 sides appeared at least once? (Hint:…

A: Consider Yi be the number of additional rolls required for a new side to appear until i-th side have…

Q: of the apples is equal to 3 of the oranges. If there are 12 mor 5 In a fruit stall, - - annles than…

A: Fraction:  A small part of something.  In other words, numerical value that is not a whole number A…

Q: If n is an integer greater than 2, then for all integers m, n does not divide m or n + m # nm.

A: c Given n∈Zand n>2. We have to prove that for all m∈Z, n/m or n+m/nm. Suppose n/m and…

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 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: Suppose there are 10 students participating in a workshop that meets every day of a five-day work…

A: Given that there are 10 students participating in a workshop that meets every day of a five-day work…

Q: A1. How many integers, greater than or equal to10000 but less than or equal to 39999, can be formed…

A: Since you've asked multiple parts questions, as per our answering guidelines we are supposed to…

Q: 5. Demonstrate that Im(iz) = Re(z).

A: It is required to demonstrate the problem 5. Problem 5 is solved below in detail.

Q: * 10. Is the following proposition true or false? Justify your conclusion. For each integer n, n is…

A:

Q: er

A: To find all the permutations of the 4 objects a ,b, c, and d, taken 3 at a time.

Q: What is the set of O of odd positive integers less than 10?

A: The odd positive integers less than 10 are 1, 3, 5, 7, 9.

Q: A box contain 8 red and 6 green balls. In how many ways can 3 balls be drawn such that 2 is ed and 1…

A: Answer - A box contains 8 red and 6 green balls.                 How many ways can 3 balls be drawn…

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: Let S be the set of positive integers less than 500. Find the number of integers in S that are…

A:

Q: Suppose that you toss a fair coin 10,000 times. Write down explicitly the at the coin lands on heads…

A: Given information: Given that a fair coin is tossed 10,000 times.

Q: how many are the possible cases, regardless of

A: From the given information, The coin is tosses n times. And the coin has two faces.

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.