Given six distinct pairs of gloves, 12 distinct gloves in all, how many ways are there to distribute two gloves to each of six sisters

a) if the two gloves someone receives might both be for the left hand or right hand.

b) if each sister gets one left and one right.

Soln:

a) So i thought about dissectng the problem first into finding the number of ways in which I could make pairs of gloves:

C (12, 2)

then I asked how many ways could the sets of gloves be assigned amongst the 6 sisters:

6! 6!

and taking the product of this would give me the amount of ways this could occur:

= C (12,2) * 6!

then for part b)

using this same idea except:

C (6,1) C (6,1) for the left and right glove each.

the C (6,1) * C (6,1) * 6!

Right way to think them through?