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1.In how ways can the following persons be seated in a round table? a. 7 persons b. 9 persons c. 10 person d. 13 persons e. 15 persons 2. In how many ways can the following number of keys be arranged? a. 6 keys b. 8 keys c. 11 keys d. 12 keys e. 17 keys

1.In how ways can the following persons be seated in a round table? a. 7 persons b. 9 persons c. 10 person d. 13 persons e. 15 persons 2. In how many ways can the following number of keys be arranged? a. 6 keys b. 8 keys c. 11 keys d. 12 keys e. 17 keys

Advanced Engineering Mathematics
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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### Seating Arrangements and Arrangements of Objects #### 1. In how many ways can the following persons be seated in a round table? - a. 7 persons - b. 9 persons - c. 10 persons - d. 13 persons - e. 15 persons This question involves calculating the number of unique seating arrangements in a circular formation. For n people seated around a round table, the number of arrangements is given by the formula \((n-1)!\). #### 2. In how many ways can the following number of keys be arranged? - a. 6 keys - b. 8 keys - c. 11 keys - d. 12 keys - e. 17 keys This question relates to calculating the number of permutations of a set of distinct objects (keys). For any given number of keys \(n\), the total number of permutations is given by \(n!\).
Transcribed Image Text:### Seating Arrangements and Arrangements of Objects #### 1. In how many ways can the following persons be seated in a round table? - a. 7 persons - b. 9 persons - c. 10 persons - d. 13 persons - e. 15 persons This question involves calculating the number of unique seating arrangements in a circular formation. For n people seated around a round table, the number of arrangements is given by the formula \((n-1)!\). #### 2. In how many ways can the following number of keys be arranged? - a. 6 keys - b. 8 keys - c. 11 keys - d. 12 keys - e. 17 keys This question relates to calculating the number of permutations of a set of distinct objects (keys). For any given number of keys \(n\), the total number of permutations is given by \(n!\).
Expert Solution
Question 1

We know that,

The number of ways n persons can be seated in a round table is (n-1)!

a.

7 persons can be seated in a round table in (7-1)! ways = 6! ways = 720 ways

b.

9 persons can be seated in a round table in (9-1)! ways = 8! ways = 40,320 ways

c.

10 persons can be seated in a round table in (10-1)! ways = 9! ways = 362,880 ways

d.

13 persons can be seated in a round table in (13-1)! ways = 12! ways = 479,001,600 ways

e.

15 persons can be seated in a round table in (15-1)! ways = 14! ways = 87,178,291,200 ways

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