3. A password is a sequence of letters (a-z) and digits (0-9). Find the number of passwordsof length 10 under the constraints in (a), (b) or (c) (three separate problems). Expressyour answer using factorials and integers, products and ratios of them, and/or sums ofsuch things.There are 3 letters and 7 digits, and at most one '9'.(b) There are 6 letters and 4 digits, and no digit occurs twice.(c) No letters are used BUT the first four digits are not all the same AND the last fourdigits are not all the same, AND the 4th, 5th, 6th and 7th digits are not all thesame.

Given that the number of letters (a-z) and the digits (0-9) is used to form a password of length…

Answered: 3. A password is a sequence of letters…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The fourth door is very tricky. It has a 4-number lock to escape consisting of the numbers from 1 to 36. Here are your clues: a. The first number is the sum of the digits in the year that Gottfried Leibniz published his works on Calculus. c. The third number is the sum of the digits of the year that Newton died. d. The last number is the 5th and 6" decimal digits in order of V57.
17. In September, October, and November, a student solves at least one problem per day but not more than 13 problems per week. Show that she solves exactly 12 problems on some set of consecutive whole days.
A number in Z+is written on the back of each of three cards. The numbers are not necessarily different but the sum of the three numbers is 14. Each card is flipped backwards so that the number cannot be seen by anyone. Carter, Mars, and Mann each select one of the cards, being careful not to let the other two see the number that is on the card. Carter says, after looking at his card, “I know that Mars and Mann have different numbers.” Mars then says, “I already knew that thet hree cards had different numbers.” At this point, Mann confidently exclaims, “I now know all thet hree numbers!” What were the numbers and who had which number?
Problem #5. In how many ways can a committee consisting of 2 managers and 3 staff members be formed if there are 6 managers and 10 staff members who are eligible to serve on the committee.
A twenty-something single person is planning a ski vacation. Assume that he has 2 possible destinations: Utah, and Oregon. There are 4 ski areas in Utah with 4 available times for 3 of the areas, and 1 times for the other area. There are 4 ski areas in Oregon with 2 available times for 3 of the areas, and 4 times for the other area. (A "time" refers to a weekend for which there are vacancies at the ski lodge.) A trip plan involves the selection of a location, ski area, and a time. How many possible plans are there?
The problem constraint arising from labor contracts has the form ax + byc, for some values a, b, c, and some sign . Find a, b, □, and c. a = [Select] b = [Select] C= [Select] [Select]
You, Alice and Bob are engineering a solution the Really Hard Problem and have come up with ten algorithmic solutions. Alice has analysed the code and expressed the run times of the ten solutions with the following ten functions: •fo(n) = (3n+3)³ • fi(n) = [₁2² f2(n) = n². (22+75) • f3(n) = 3log, n • f4(n) = fs(n) = log₂ (n^²) • fe(n) = log₂ (n² +5n-3) • fr(n) = log₂ (log₂ n+3) f8(n) = 2 f9(n) = 2222 a) Alice has asked you to help her classify these functions based on their asymptotic growth rate. That is, she wants you to prove a tight big-Theta bound for each function by following these steps. i. Use algebra to simply the function for ease of analysis. Remember the goal of simplification is to isolate terms and identify the dominant term. For instance, we might want to expand (n + 1)² to n² +2n+ 1 to see that n² is the dominant term. ii. Use your intuition, the limit test, or algebra to come up with a good guess of a tight bound. For instance, after isolating n² as the dominant term…
For this problem, assume the cooler contains 28 cans, 10 of which are regular, and the rest of which are diet. (1) How many ways can you choose 5 cans from the cooler? (2) How many ways can you choose 5 regular cans from the cooler? (3) How many ways can you choose 5 diet cans from the cooler? (4) How many ways can you choose 5 cans from the cooler so that at least 4 are diet?

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