Кeys We have a box with 21 keys. There are 7 types of keys. Each key is colored (monochromatic) in one of 3 colors: red, grcen, or blue. Thus, the box contains exactly one key of cach combination of type and color. We pick a subsct of keys from the box. For cach of the following seven questions, count the number of ways that we can pick a subset satisfying the listed constraints. Your answers must be given in terms of binomials and exponentials. Do not give your answers in terms of factorials. Do not simplify your answers into a single integer. You must use binomials and exponentials. Use the notation (:) for binomials. justify cach of your seven answers, and show your calculations. Formal proofs are not required.

Кeys We have a box with 21 keys. There are 7 types of keys. Each key is colored (monochromatic) in one of 3 colors: red, grcen, or blue. Thus, the box contains exactly one key of cach combination of type and color. We pick a subsct of keys from the box. For cach of the following seven questions, count the number of ways that we can pick a subset satisfying the listed constraints. Your answers must be given in terms of binomials and exponentials. Do not give your answers in terms of factorials. Do not simplify your answers into a single integer. You must use binomials and exponentials. Use the notation (:) for binomials. justify cach of your seven answers, and show your calculations. Formal proofs are not required.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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You are given a 2 by n grid, where the cell on row i column j contains a non-negative number ai,j . You can start at either cell in the lefttmost column, and your goal is to reach either cell in the rightmost column by a sequence of moves. You can move to an adjacent cell (if it exists) in each of the 4 cardinal directions (up,down, left and right). A path achieves a score equal to the sum of values in its cells. Note that a cell which is used twice in a path only counts its value once to the score of that path.Design an algorithm which runs in O(n) time and finds a path of minimum score from the leftmost column to the rightmost column.
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Correct answer will be upvoted else Multiple Downvoted. Computer science. player begins the game from the 1-st stage and should beat the stages in expanding request of the stage number. The player dominates the match in the wake of beating the n-th stage. There is all things considered one designated spot on each stage, and there is consistently a designated spot on the 1-st stage. Toward the start of the game, just the designated spot on the 1-st stage is initiated, and any remaining designated spots are deactivated. At the point when the player gets to the I-th stage that has a designated spot, that designated spot is initiated. For each attempt of a phase, the player can either beat the stage or bomb the stage. On the off chance that they beat the I-th stage, the player is moved to the i+1-st stage. On the off chance that they bomb the I-th stage, the player is moved to the latest designated spot they actuated, and they need to beat the stages after that designated spot once…
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A deck of cards contains 52 cards with four suits: club, diamond, heart and spade ranging in values from 2, ... to 10, Jack, Queen, King and Ace. Ace has the highest value in the same suit. Cards can be compared using the face value. A card with higher face value is bigger than a card with lower face value. If two cards have the same face value, then the suit determines the order. Club is smaller than diamond which is smaller than heart which is smaller than spade. For example: club 2 < diamond 2 < heart 2 < spade 2 if compared. Write an interactive Java program that allows a user to randomly pick a card from the deck of 52 cards (using a random number between 1 and 4 to represent the four suits: club, diamond, heart and spade and then another random number to represent the face value) to play. Show the suit and face value of the user card. Then the program acts as a card dealer which randomly draws another card and displays the card (again showing the suit and face value of…
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You are the chief commander of US Army; you have been deployed in an ongoing war training of defusing the mine. Mines are placed on the ground which can be considered as a gird of size N*M. Each block (i, j) has a mine in it if and only if the summation of the block coordinates is divisible by 2. Your task is to move from the first row to the last row. The mines will not blow if the given rules are followed: • If you are on even row you can move to any cell that is in the neighborhood • If you are on odd row, you can only go the odd row that has mine on that and same with the unmined row. You have to develop a python program to calculate the number of ways to reach row number N starting from row number 1. Test Cases: 4 8 Output: 10
In stores, boxes should be placed in an organized way otherwise it will be messy. Given a collection of boxes, it is requested to place them on top of each other to reach the minimum possible height. There is a condition, where a box cannot be placed on top of another box unless the area of its 2D base is smaller or equal of the 2D base of the lower box. It is allowed to rotate any box to use any two sides as its base. For example, consider below 4 boxes where each box has the following dimensions Input: Box 1: (2,1,3), Box 2:(6,3,8) Box 3: (4,2,5), Box 4:(3,1,6), Output: From bottom to top as follows: In the bottom → Box 2 on the base (6,8) and height 3, On top of it → Box 3 on the base (4,5) and height 2, Then → Box 4 on the base (6,3) and height 1, Finally → Box 1 on the base (2,3) and height 1. The total height is 7 [Explanation: as we can see that the first box in the bottom is the box 2 with base 6x8 and height 3, then box3 with base 4x5 and height 2, and so on. This arrangement…
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