Fashion problem from hell ! (Combinations Problem)

[TaTum]

Does any guru know how to solve this problem?

--
Dave has no fashion sense, and will wear any combination
garments regardless of whether someone thinks they "match".
Everyday Dave chooses an outfit consisting of one of each
of the following garments:
jacket, tie, shirt, pants, boxers, right sock, left sock,
right shoe, left shoe. If Dave has more than one of each of
the listed garments, and can make 63,000 different outifts,
then for how many garments does Dave have exactly five choices?

A. 0
B. 1
C. 2
D. 3
E. 4


Official Answer:

SPOILER: D

?!?!?

[piju]

Not a guru ..but here is a shot.
Let the number of each garment be: g1, g2,...,g9
The quantity of outfits using the different garments is
g1xg2xg3x...g9=63000 --> g1xg2x..g9 = 2x2x2x3x3x5x5x5x7
By breaking the nbr in prime factors we can see they're exactly nine factors (All of them greater than 1).
So every factor must correspond to the quantity of every garment.

As you see there are 3 garments with 5 choices. Answer D

[TaTum]

Oh! I got it now. I didn't clearly understand the question at the beginning.
Thank you very much!

[nikiforos]

Another vote for D
factorise 63000 to get 2^3.3^2.5^3.
Also we know that each of the items ahs more than one of it's type and there are 9 items in all.
So items having exactly 5 are 3.

[ken_english]

good one

[ameyal]

too good...

[MTG123]

Another vote for D