Dave has 10 poker chips, 5 of which are red and the other 5 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 considered distinct if one can be flipped to appear identical to the other?

 -    

Step-by-step explanation:

Given:

10 poker chips:

Let the stack has positions (1,2,3,4,5,6,7,8,9,10)

So we can find all possible outcomes of the stack is: =

and the possibility of a stack to be identical while flipping is:

So the different 10-chip stacks can Dave make if two stacks are not considered distinct:

 -  

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743