Howdy!

I have a set of 8 objects: {A, B, C, D, E, F, G, H}

I have 6 buckets.

I must place all 8 objects in any combination of the 6 buckets.

I can place between 0 and 4 objects in any bucket.

I must place all objects in a bucket.

A and B cannot be placed in the same bucket.

C and D cannot be placed in the same bucket.

E and F cannot be placed in the same bucket.

F and G cannot be placed in the same bucket.

The order of objects in the bucket is irrelevant. (Bucket 1: ACEF is identical to Bucket 1: FECA, i.e.)

The order of buckets is irrelevant. (Bucket 1: ACEF, Bucket 2: BDEG is identical to Bucket 1: BDEG, Bucket 2: ACEF is identical to Bucket 4: BDEG, Bucket 6: ACEF, i.e.)

The question is: how many arrangements exist? How do I figure this one out?