16 people are seated evenly around a circular table. To choose teams for a game, 8 (identical) white cards and 8 (identical) black cards are distributed among the people. If each person gets the same color as the person seated directly across from them, how many was can the cards be distributed?
Your answer for this problem was 70, because you assumed that for any given half, there must be 4 white cards and 4 black cards. However, this is false, for example, if one half of the table has all black cards, and the other half has all white cards. Since you can deal one of two colors to each person in half of the table, and the other half of the table is determined, then the answer is 2^8=256. Because algebra, there is 8 of each type of card dealt.