In how many ways can three pairs of different colored socks be removed from a drawer, one sock at a time?

Answer 1

Letting A be one sock of color 1, B be one sock of color 2, and C be one sock of color 3, here is a list of the 54 possible combinations:

AABBCC

AABCBC

AABCCB

AACCBB

AACBCB

AACBBC

ABABCC

ABACBC

ABACCB

ACACBB

ACABCB

ACABBC

BAABCC

BAACBC

BAACCB

CAACBB

CAABCB

CAABBC

BBAACC

BBACAC

BBACCA

BBCCAA

BBCACA

BBCAAC

BABACC

BABCAC

BABCCA

BCBCAA

BCBACA

BCBAAC

ABBACC

ABBCAC

ABBCCA

CBBCAA

CBBACA

CBBAAC

CCAABB

CCABAB

CCABBA

CCBBAA

CCBABA

CCBAAB

CACABB

CACBAB

CACBBA

CBCBAA

CBCABA

CBCAAB

ACCABB

ACCBAB

ACCBBA

BCCBAA

BCCABA

BCCAAB