397643151/2 |-161% +1. Verify that the following three tableaux are all rook-equivalent.[Recall that two tableaux are said to be rook-equivalent if for each k N there is thesame number R of ways to place k non-attacking rooks on each tableau.]X ...13

Given: The three tableaux To Verify: The three tableaux are all rook-equivalent.…

Answered: 1. Verify that the following three…

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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“ You are dealt five cards from a standard deck of 52 cards. How many of these handshave at least one queenandat least one spade. ”He breaks this into two cases. In the first case, he looks at hands which contain the queen of spadesQ♠. There is 1 way of choosing the Queen of Spades, and51C4ways of choosing the other fourcards. In the second case, he will start by choosing a non-spade queen (3 ways) and a non-queenspade (12 ways). There are 50 cards remaining, so he also throws away the Queen of Spades sothat he doesn’t overlap case 1. This gives49C3ways of choosing the last three cards. He concludesthat the answer is51C4+ (3·12·49C3). His answer is incorrect. Explain why, and give the correctanswer.
3. How many ways can we place 7 nonattacking rooks on the 7 by 7 chessboard below, with forbidden positions as shown?
A bag contains four red marbles, two green ones, one lavender one, three yellows, and three orange marbles. HINT [See Example 7.] How many sets of four marbles include none of the red ones? sets
A bag contains five red marbles, three green ones, one lavender one, three yellows, and two orange marbles. HINT [See Example 7.] How many sets of four marbles include none of the red ones?
A movie studio is scheduling the release of six films-Fiesta, Glaciers, Hurricanes, Jets, Kangaroos, and Lovebird. No two of these films can be released on the same date. The release schedule is governed by the following conditions: Fiesta must be released earlier than both Jets and Lovebird. Kangaroos must be released earlier than Jets, and Jets must be released earlier than Hurricanes. Lovebird must be released earlier than Glaciers. 3. If Glaciers is released earlier than Hurricanes, then each of the following could be true except: A Glaciers is released fourth. Ⓑ Jets is released third. C Kangaroos is released second. D Lovebird is released third. E Lovebird is released fifth.
Six European language classes (Deutsch, Français, Español, Italiano, Afrikaans, and Magyar Nyelv) need to schedule study groups. The schedule must be able to accommodate all students attending the six classes, that is, study groups cannot be placed in the same hour if they have a common student. The following table shows which classes have students in common (marked with an X): Deu Fr EspItAf MN X X x X X X Esp X X X X Deu Fr X XX It X X Af X X X X MN X X XX Assuming that each study group meets for an hour, which of the following schedules accomplishes these group meetings in the least possible number of hours and without student conflict. Select one: O A. (1: Deutsch, Français, Español), (2: Italiano, Afrikaans, Magyar Nyelv) O B. (1: Deutsch, Italiano), (2: Français, Afrikaans), (3: Español, Magyar Nyelv) Oc. (1: Deutsch, Magyar Nyelv), (2: Français, Italiano), (3: Español, Afrikaans) O D. (1: Deutsch), (2: Français), (3: Español), (4: italiano), (5: Afrikaans), (6: Magyar Nyelv) O…
At the beginning of a game of chess, the back row consists of two (identical) rooks on the corners, then two knights next to them, then two bishops, and finally a king and a queen in the center. Bobby Fischer, an American chess legend, popularized the idea of randomly shuffled starting positions. Inhow many distinct ways can the eight pieces above be aligned?

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1. Verify that the following three tableaux are all rook-equivalent. [Recall that two tableaux are said to be rook-equivalent if for each k N there is the same number R of ways to place k non-attacking rooks on each tableau.]