Seven friends are seated around a circular table at a wedding reception. In how many ways can they be arranged if:  a. two particular people must sit together?  b. two particular people must not sit beside each other?  c. they are seated around a table relative to a widow?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Identify each problem as Permutation, combination, or both permutatin and combination problem. 

 
4. Seven friends are seated around a circular table at a wedding reception. In how many ways can they be arranged if: 
a. two particular people must sit together? 
b. two particular people must not sit beside each other? 
c. they are seated around a table relative to a widow? 

5. A student in senior high school is to select 2 electives for the first semester. 
a. In how many ways can the student select 2 electives from 5 offered electives? 
b. In how many ways can the student select one elective with a Monday - Thursday schedule and another elective scheduled every Tuesday - Friday from the 5 electives, if all 5 electives have available schedules on all given days? 
c. In how many ways can this be done if the student must select 1 elective out of 3 morning electives and another elective out of the 2 afternoon electives? 

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