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A group of 5 friends—Archie, Betty, Jerry, Moose, and [#permalink]
 29 Sep 2012, 13:42
Question Stats:
36% (02:45) correct
64% (01:01) wrong based on 0 sessions
A group of 5 friends—Archie, Betty, Jerry, Moose, and Veronica—arrived at the movie theater to see a movie. Because they arrived late, their only seating option consists of 3 middle seats in the front row, an aisle seat in the front row, and an adjoining seat in the third row. If Archie, Jerry, or Moose must sit in the aisle seat while Betty and Veronica refuse to sit next to each other, how many possible seating arrangements are there? A. 32 B. 36 C. 48 D. 72 E. 120
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Re: A group of 5 friends—Archie, Betty, Jerry, Moose, and [#permalink]
29 Sep 2012, 15:11
smartass666 wrote: A group of 5 friends—Archie, Betty, Jerry, Moose, and Veronica—arrived at the movie theater to see a movie. Because they arrived late, their only seating option consists of 3 middle seats in the front row, an aisle seat in the front row, and an adjoining seat in the third row. If Archie, Jerry, or Moose must sit in the aisle seat while Betty and Veronica refuse to sit next to each other, how many possible seating arrangements are there?
32
36
48
72
120 First, place one person in the isle seat - 3 possibilities. Second, place the two girls Betty and Veronica (more specifically separate them) and then place the remaining two persons - the girls can sit either in the middle seats, one seat apart, or one girl in the third row and then the other girl with the remaining two guys in the middle seats - which is 2*2! + 2*3! = 16. Total number of possibilities 3*16 = 48. Answer C.
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Re: A group of 5 friends—Archie, Betty, Jerry, Moose, and [#permalink]
07 Dec 2012, 19:19
EvaJager wrote: smartass666 wrote: A group of 5 friends—Archie, Betty, Jerry, Moose, and Veronica—arrived at the movie theater to see a movie. Because they arrived late, their only seating option consists of 3 middle seats in the front row, an aisle seat in the front row, and an adjoining seat in the third row. If Archie, Jerry, or Moose must sit in the aisle seat while Betty and Veronica refuse to sit next to each other, how many possible seating arrangements are there?
32
36
48
72
120 First, place one person in the isle seat - 3 possibilities. Second, place the two girls Betty and Veronica (more specifically separate them) and then place the remaining two persons - the girls can sit either in the middle seats, one seat apart, or one girl in the third row and then the other girl with the remaining two guys in the middle seats - which is 2*2! + 2*3! = 16. Total number of possibilities 3*16 = 48. Answer C. Could you please elaborate on this further. I am still stuck with the question.
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Re: A group of 5 friends—Archie, Betty, Jerry, Moose, and [#permalink]
08 Dec 2012, 05:19
smartass666 wrote: A group of 5 friends—Archie, Betty, Jerry, Moose, and Veronica—arrived at the movie theater to see a movie. Because they arrived late, their only seating option consists of 3 middle seats in the front row, an aisle seat in the front row, and an adjoining seat in the third row. If Archie, Jerry, or Moose must sit in the aisle seat while Betty and Veronica refuse to sit next to each other, how many possible seating arrangements are there?
32
36
48
72
120 I also struggle with probability and combinations  Need some more input from some one
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Re: A group of 5 friends—Archie, Betty, Jerry, Moose, and [#permalink]
23 Dec 2012, 14:44
A,J, M & B,V AISLE SEAT X THIRD ROW X FIRST ROW Case 1: B/V sit in third row 3 * 2 * 3*2*1 = 36 Case 2: B/V sit in first row 3 * 2 * 2*1*1 = 12 Total ways = 36 +12 = 48 Hence C
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Re: A group of 5 friends—Archie, Betty, Jerry, Moose, and [#permalink]
24 Dec 2012, 09:38
aditi2013 wrote: EvaJager wrote: smartass666 wrote: A group of 5 friends—Archie, Betty, Jerry, Moose, and Veronica—arrived at the movie theater to see a movie. Because they arrived late, their only seating option consists of 3 middle seats in the front row, an aisle seat in the front row, and an adjoining seat in the third row. If Archie, Jerry, or Moose must sit in the aisle seat while Betty and Veronica refuse to sit next to each other, how many possible seating arrangements are there?
32
36
48
72
120 First, place one person in the isle seat - 3 possibilities. Second, place the two girls Betty and Veronica (more specifically separate them) and then place the remaining two persons - the girls can sit either in the middle seats, one seat apart, or one girl in the third row and then the other girl with the remaining two guys in the middle seats - which is 2*2! + 2*3! = 16. Total number of possibilities 3*16 = 48. Answer C. Could you please elaborate on this further. I am still stuck with the question. Hi, I used the following method, please confirm this method though as this is one of my weak areas...:- Consider the following seating arrangement:- S1, S2 S3, S4 and S5 (aisle) Now, as per one of the restrictions, S5 can be filled in 3 ways only, and once it is filled, no other arrangement is possible ( as it is one seat) Therefore, S5 (fill) = 3ways We are now left with 4 seats and 4 individuals: Number of ways of selecting 4 individuals to fill 4 seats = 4C4 = 4 ways Moreover, among those 4 individuals, we can have 4! arrangements = 24 arrangements Therefore, the total arrangements = 24 *4 = 72 arrangements -----This is only when the second restriction is in effect Lets us now, consider restriction 1: Betty and Veron are never together No of arrangements when betty and veron are never together = (Total number of arrangements) - (No of arrangements when betty and veron are always together) When betty and Veron are always together: Consider both one entity, Lets say = X there fore, now we have 4 seats and 3 people: Number of ways 3 peoplefill 4 seats = 4C3 = 4 ways Number of arrangeents among those 3 people = 3! = 6 arrangements Therefore, total number of arrangements when Betty and Veron sit together are = 4* 6 = 24 arrangements =>No of arrangements when betty and veron are never together = 72 - 24 = 48 arrangements Hope this helps....
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Re: A group of 5 friends—Archie, Betty, Jerry, Moose, and [#permalink]
13 Jan 2013, 03:23
Hey...I am not able to understand the explanations given
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Re: A group of 5 friends—Archie, Betty, Jerry, Moose, and
[#permalink]
13 Jan 2013, 03:23
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