In how many ways can an odd number of toys be selected from 13 different toys?

Correct answer: 4096

The governing concept is the equal division of all subsets into even-cardinality and odd-cardinality subsets. Each of the 13 distinct toys has two possibilities: selected or not selected. Therefore, the total number of subsets is 2^13 = 8192, including the empty subset. To see why the odd and even counts are equal, pair every subset with the subset obtained by toggling one fixed toy: if the original subset has even size, the paired subset has odd size, and vice versa. Thus exactly half of all subsets have odd size. The required number is 2^13/2 = 2^12 = 4096, so option C is correct. Option D counts all subsets, and option B excludes only the empty set but still includes even-sized nonempty subsets.