Question

Dave has 10 poker chips, 6 of which are red and the other 4 of which are white. Dave likes to stack his chips and flip them over as he plays. How many different 10-chip stacks can Dave make if two stacks are not consider distinct if one can be flipped to appear identical to the other

Answer 1

The number of 10 chips stacks that Dave can make if two stacks are not considered distinct is 110.

The solution

To get the symmetric stacks, one has to subtract the symmetric stacks to know the ones that are asymmetric.

The symmetric are flipped. Given that they are double counted what we have to do is to divide through by 2.

6/2 = 3

10/2 = 5

4/2 = 2

1/2(10C6) - (5C3) + (5C3)

0.5(210-10+10)

= 110