Questions 17-18. There are 20 seats in the froat row of s small theater There ac
ID: 3303180 • Letter: Q
Question
Questions 17-18. There are 20 seats in the froat row of s small theater There ace & odividoals that wil be sitting in the front row . In how many unique ways can the froat sow seating arrangemest be made if empty seats aze not distinguishable from each other and there is no restriction on which seats ena be left a) 27,907,200 b) 38,760 c) 338 × 1015 d) 4845 e) 232,560 18. In how many unique ways can the frost row seating arrangement be made if empty seats are not distinguishable from each other but the thester manager waats the two end seats of the front row always filled because it makes it appear to have a funer- a) 13,366,080 b) 73,440 e) 2,203,200 d) 111,384 e) 3060Explanation / Answer
Number of seats = 20
Number of individuals to be seated = 6
17. The first person can sit in any of the 20 seats.
The second person can sit on any of the 19 remaining seats
and so on.
Total number of arrangements = 20*19*18*17*16*15 (or 20P6)
= 27,907,200
which is given in option a)
18. The left end can be filled by any of the 6 people.
The right end can be filled by any of the 5 people as one person has taken the left end seat.
Now the question reduces to problem 17 with 4 people and 18 seats.
They can occupy in 18P4 ways or 18*17*16*15 ways
= 73440
=> Total number of arrangements = 6*5*73440
= 2,203,200
which is given in option c)
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