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Five students Joe, Katy, Lori, Michael and Natasha must [#permalink]

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23 Jul 2006, 01:08

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Five students Joe, Katy, Lori, Michael and Natasha must stand in a line. Natasha cannot stand at either the front or back and Lori must stand in the middle. how many more combinations would there be if Lori could stand anywhere in line?

a) 12
b) 30
c) 48
d) 60
e) 72

when i tried to solve this i got:

33121 = 18 (with Lori standing in the middle)

44321 = 96 (with Lori standing anywhere)

96 - 18 = 78 isnt even an answer choice. where did i go wrong?

Five students Joe, Katy, Lori, Michael and Natasha must stand in a line. Natasha cannot stand at either the front or back and Lori must stand in the middle. how many more combinations would there be if Lori could stand anywhere in line?

a) 12 b) 30 c) 48 d) 60 e) 72

when i tried to solve this i got:

33121 = 18 (with Lori standing in the middle)

44321 = 96 (with Lori standing anywhere)

96 - 18 = 78 isnt even an answer choice. where did i go wrong?

Red part is wrong.

Second position can be occupied by 4 (All except Lori)
So it will be 3*4*1*2*1 = 24
_________________

If Lori takes the middle, then Natasha has 2 places, and the others have 3 x 2 x 1 places. In total, 12.

If Lori can go anywhere, then Natasha has 3 places, the others have 4 x 3 x 2 x 1 places. In total, 72.

Increase = 72 - 12 = 60
_________________

Uh uh. I know what you're thinking. "Is the answer A, B, C, D or E?" Well to tell you the truth in all this excitement I kinda lost track myself. But you've gotta ask yourself one question: "Do I feel lucky?" Well, do ya, punk?

_ _ _ _ _ 5 spots; plug L in the middle, so N has 2 possible spots. For each of her spots there are 3p3 possibilities for the rest. So combos are
2 x 3p3=12

next make L a little less fussy. Now N has 3 possible spots. For each position she chooses, the other 4 can have 4p4 arrangements
=3 x 4p4 = 3 x 24 = 72

With Lori in middle,total permutations to 4! (lori is in fixed position)
perms where Lori in middle, Natasha could be in back or front =3! * 2
(lori is in fixed position and Natasha has two options)
total where Lori in middle, Natasha not in back or front = 4! - (3! * 2) = 12

With Lori any where , total permutations = 5!
perms where natasha in back or front = 4! * 2
total where Natasha not in back or front = 5! - (4! * 2) = 120 - 48 = 72