In a clothing store, there are six different colored neckties (red, or

Slightly different way to think about it...

First box can take from 6 shirts and 6 ties (6*6 possibilities)
Second box can take from 5 shirts and 5 ties (since one of each was already used in the first box) (5*5 possibilities)
Third box can take from 4 shirts and 4 ties (4*4 possibilities)
etc
Total ways to pack those boxes: (6!)^2
But this counts different arrangement of boxes (1 blue shirt and 1 red tie in box 1 is different from 1 blue shirt and 1 red tie in box 2)... So we need to un-arrange, i.e. divide by 6!.

Total ways to pack the boxes = 6! = 720
Only one way to have RR, OO, YY, GG, BB, II

Answer: E

Also, if we had to guess, we could probably pick E
A. 719/720 ---> way too big
B. 1/120 ---> maybe
C. 2/233 ---> 233 in the denominator doesnt look familiar (not a square of an integer and not a factorial). also, we're looking for a '1' in the numerator
D. 3/543 ---> same logic as for C. I dont know how they could have 543 in denominator. also, we're looking for a '1' in the numerator
E. 1/720 ---> probably. and because of the complementary option A, i would think A is the trap and E is the correct answer