This is a Discrete Math Problem 22. * Consider strings of length n over the set {a, b, c, d}.a. How many such strings contain at least one pair of adjacentcharacters that are the same?b. If a string of length ten over {a, b, c, d} is chosen at random,what is the probability that it contains at least one pair ofadjacent characters that are the same?

Answered: Image /qna-images/answer/7019dfe1-9001-4a05-b7e7-a53d879d2fff.jpg

Answered: Consider strings of length n over the…

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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Number theory problem
Consider the problem "A common type of bike lock requires a six digit password, and only allows digits O through 9. How many passwords are there that contain the digit 9?" A student reasons: There are 6 possible places to put the 9, and then no restriction. So there are 105 possible arrangements of the other digits. This means the correct answer is 6 · 105. This solution is incorrect, since the student overcounts passwords containing more than one 1. This solution is incorrect, since, in the first step, the student needs to specify which digit gets the one. This solution is incorrect since there are not 10x10x10x10x10 arrangements of the digits O through 8 in the other three places. This solution is correct.
Hello, I am having trouble with this problem for my discrete math class. I have provided a snip below.
Someone has stolen an ATM card and knows that the first and last digits of the PIN are 5 and 1, respectively. He has three tries before the card is retained by the ATM (but does not realize that). So he randomly selects the 2nd and 3rd digits for the first try, then randomly selects a different pair of digits for the second try, and yet another randomly selected pair of digits for the third try (the individual knows about the restrictions described in (b) so selects only from the legitimate possibilities). What is the probability that the individual gains access to the account?
3. If you have a jar of 1000 red and blue jelly beans and you 4 1 know that P(Blue) and P(Red) = list several 5 mathematical observations you can make about the num- ber of beans in the jar.
9 (C) (a) You give your students the following problem: "You just bought 30 beads of which 18 are gold and identical and 12 are silver and identical. You want to line them up in a row. How many different arrangements of the beads can you make?" Elizabeth solves the problem by finding the number of distinguishable permutations of 30 objects, 18 alike of one kind and 12 alike of another kind. That is, she uses the result of the previous problem. Natalie solves the problem by finding the number of combinations of 30 different objects taken 18 at a time. Who is correct? (b) Does the number of permutations of n objects, ralike of one kind and n r alike of another kind, always equal the combinations of n different objects taken r at a time? Explain.
Problem 13: Find U, A¡and N,A¡ for every i, where (i) A¿ = {i, i+1, i + 2, .} (ii) A¡ = {0, i} (iii) A¿ = (0, i) i.e., the set of real numbers 0 < x < i.
DISCRETE MATH problem
Problem 4: (4.1) Show that 2"
You are looking at a math problem you did in the past with regards to Combinatorics. However, most of the work you are looking at is virtually unreadable and doesn't make sense. However, you are able to read the last line of your work. It's stated below: 20! 12! 14712 Ways. 15!5! 7!5! For this thinking evaluation, you have to come up with the original (but realistic) application word problem that could have had the above line written as the last step of the solution to this problem. To ensure maximum success, you should probably explain why you came up with the problem you did, as well as prove how the step written above must be the last line in the solution of the problem. Additionally, you probably want to talk about the step itself in terms of the mathematical components/key ideas/key features of Combinatorics that you have learned in Chapters 2 and 3. Good Luck!!
Problem 27: Show that N when z = 1 -2 2 +..+z_2 + _2 + 1 = (2)X ·+z-(N-1) 1-z-N when z + 1 1- z

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