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17 Jul 2023, 01:55
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
63% (02:08) correct
37%
(02:05)
wrong
based on 175
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In a certain movie theater, the rows are 7 seats across with aisles on either side. A group of 6 friends goes to the movies and finds an empty row to sit in. One of them needs to sit in a seat along the aisle. Which of the following calculations represents the number of possible different seating arrangements for the 6 friends?
A. 360
B. 720
C. 1,440
D. 5,040
E. 10,080
A. 360
B. 720
C. 1,440
D. 5,040
E. 10,080
19 Jul 2023, 13:41
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Bunuel
\(2_C_1\)*\(6_C_5 \)* \(5!\)\(= 2*6*120 =1440\)
\(2_C_1= \)Choosing one seat from the two aisle seats for that one person.
\(6_C_5=\) Choosing \(5\) seats from the remaining \(6\) seats
\(5! =\) # of ways to arrange those five seats.
Hope it helps.
19 Jul 2023, 15:21
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First, we must select which side the person sitting along the aisle is on. There are 2 sides, so there are 2 options.
Next, of the remaining 6 seats, we need to choose 5 for the seats that will be filled. 6C5 = 6!/5! = 6 total ways.
Within those 5 seats, the total number of ways to arrange the 5 friends = 5! = 5*4*3*2*1 = 120.
So, the total number of arrangements is 2*6*120 = 1,440. Answer C.
Next, of the remaining 6 seats, we need to choose 5 for the seats that will be filled. 6C5 = 6!/5! = 6 total ways.
Within those 5 seats, the total number of ways to arrange the 5 friends = 5! = 5*4*3*2*1 = 120.
So, the total number of arrangements is 2*6*120 = 1,440. Answer C.
