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Eurovision permutations (650+)

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by Night reader » Sat Dec 04, 2010 8:15 pm
Mark is a hotel administrator, and he is making room reservations for five participants of the Eurovision song contest. The number of rooms available for the participants is five on the fifth-room floor; the contest manager requires Mark to accommodate all participants so that no male participant's room neighbors other male participant's one. In how many ways can Mark arrange five rooms among three male and two female participants?

A. 24
B. 16
C. 12
D. 48
E. 30
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by beat_gmat_09 » Sat Dec 04, 2010 8:22 pm
Night reader wrote:Mark is a hotel administrator, and he is making room reservations for five participants of the Eurovision song contest. The number of rooms available for the participants is five on the fifth-room floor; the contest manager requires Mark to accommodate all participants so that no male participant's room neighbors other male participant's one. In how many ways can Mark arrange five rooms among three male and two female participants?

A. 24
B. 16
C. 12
D. 48
E. 30
Question asks how many ways to arrange - MFMFM
No. of ways - 3*2*2*1*1 = 12
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by Night reader » Sat Dec 04, 2010 8:25 pm
Viva!

correct answer C.
thanks
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by Rahul@gurome » Sat Dec 04, 2010 8:27 pm
This means that if the rooms are numbered 1 to 5, the males will occupy first, third and fifth rooms and the females will occupy second or fourth rooms.
The number of ways this can be done is 3!*2! = 12.
The correct answer is C.
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by Night reader » Sat Dec 04, 2010 8:28 pm
Rahul@gurome wrote:This means that if the rooms are numbered 1 to 5, the males will occupy first, third and fifth rooms and the females will occupy second or fourth rooms.
The number of ways this can be done is 3!*2! = 12.
The correct answer is C.
Rahul, I found it more useful to work with diagrams for permutations rather going through combining and separating events:

___.....___.....___.....___.....___......___
F(3).....M(2).....F(2)....M(1)....F(1).....M(1)

3*2*2*1*1*1=12
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by goyalsau » Sun Dec 05, 2010 2:02 am
Night reader wrote:
no male participant's room neighbors other male participant's one.
There was a time when its said No female participant will neighbor Male Participant, But Now everything is changed, POOR GIRLS........ :D
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