Five students Joe, Katy, Lori, Michael and Natasha must

Question

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:

 3   3   1   2   1  = 18 (with Lori standing in the middle)

 4   4   3   2   1  = 96 (with Lori standing anywhere)

96 - 18 = 78 isnt even an answer choice. where did i go wrong?

ps_dahiya · Answer

Red part is wrong.

Second position can be occupied by 4 (All except Lori)
So it will be 3*4*1*2*1 = 24

kevincan · Answer

There's a problem with this, if Natasha doesn't go in place two, she must go in place 4

ps_dahiya · Answer

Got it. Thanks Kevin. I think its time to sleep.

When Lori is NOT in middle:
NXXXX - 4!
XXXXN - 4!
Total = 5! - 2*4! = 72

When Lori is in middle
NXLXX - 3!
XXLXN - 3!
Total = 4! - 2*3! = 12

Final answer = 72-12 = 60

paddyboy · Answer

D.

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

Futuristic · Answer

Straight D

_ _ _ _ _ 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

difference = 72 -12 = 60

bondguy · Answer

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

answer = 72 - 12 = 60

Five students Joe, Katy, Lori, Michael and Natasha must

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards