Dave has no fashion sense, and will wear any combination of garments regardless of whether someone thinks they “match.” Every day 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 outfits, then for how many garments does Dave have exactly five choices?
Pick.
A) 0  B) 1  C) 2  D) 3  E) 4
There are 9 different kinds of clothes.   so if you find the prime factors of 63000   i.e. 3 * 3 * 7 * 2 * 2 *2 *5 * 5 *5 * 1   But the guy has everything greater than 1... so ignoring that there are exactly   9 factors.   and 5 is 3 times.   so Answer is 3.
<result>D</result>
Dave has no fashion sense, and will wear any combination of garments regardless of whether someone thinks they “match.” Every day 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 outfits, then for how many garments does Dave have exactly five choices?