83. You are hosting a movie party, where there will be 8 persons in a room with
ID: 3209005 • Letter: 8
Question
83. You are hosting a movie party, where there will be 8 persons in a room with 8 places to sit. How many different ways are there to seat the people? 84. You are hosting a movie party, where there will be 8 persons in a room with 10 places to sit. How many different ways are there to seat the people? 85. You are hosting a movie party, where there will be 14 persons. You have 10 chairs up front, and the remaining four people will need to sit on the couch in the back. How many possibilities do you have for selecting 4 people to sit on the couch? 86. There are 10 seats for 10 people at your wedding. How many ways are there to seat them? 87. There are 10 seats for 10 people at your wedding. You have decided where to seat 3 of the people. How many ways are there to seat the rest? 88. There are 10 seats for 10 people at your wedding. However, 3 of the people each need to be in a specific seat (i.e. for each of these persons, there is exactly one seat that they need to occupy). What proportion of possible seating arrangements satisfy this condition?
Explanation / Answer
Solution:-
85) The different ways are there to seat the people is 40320.
Total seats = 8
Total people = 8
The different ways are there to seat the people = 8P8 = 8! = 40320
86) The different ways are there to seat the people is 1,814,440.
Total seats = 10
Total people = 8
The different ways are there to seat the people =10P8 = 1,814,440
87) The different ways of selecting 4 people to sit on the couch is 1,001
Total people = 14
Number of people to be selected = 4
The different ways of selecting 4 people to sit on the couch = 14C4 = 1,001
88) The different ways in which 7 people be seated is 5,040.
Total seat left = 7
Total people left = 7
The different ways in which 7 people be seated = 7! = 5,040
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