All elements within the green circle are members of A.
All elements within the blue circle are members of B.
All elements within the red circle are members of C.

Let t,u,v,w,x,y,z represent the number of members in each of the regions.

>>...Sets A, B , and C have 6 members in common...<<

That is the region with x in it because that is the only region
that is inside all three circles, so we put x=6 there, like this:



>>...Sets A and B have a total of 17 members in common...<<

The only regions common to A and B are the ones with x elements
and u elements.  Since x=6, u must be 17-6 or 11.  So we put
u=11 in there, like this:



>>...Sets B and C have a total of 10 members in common...<<

The only regions common to B and C are the ones with x elements
and y elements.  Since x=6, y must be 10-6 or 4.  So we put
y=4 in there, like this:




>>...each members of set B is contained in at least one of the other two sets...<<

This tells us that the region with v in it has no elements at all, because
if it had any elements, they would be members of B that were not contained
in either of the other two sets, so therefore we know that v=0, so we
write v=0 in that region:



>>...how many members are in set B?...<<

Now we know how many elements are in each of the regions of B,
they are u,v,x,and y, and since we know that u=11, v=0, x=6, and
y=4, then the number of elements in B is u+v+x+y = 11+0+6+4 = 21.

Answer: B has 21 elements.

Edwin