Let S = {1, 2, 3, ..., 12}. How many subsets of S, excluding the empty set, have an even sum but not an even product?

Step-by-step explanation:

The set S = {1, ,2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. The total number of elements in the set (n) is 12. The sum of the elements in the set S is even if the sum of the elements of the complement of the set S is odd.

The number of pairs that can give an even sum is therefore

Since the empty set is excluded, The number of pairs that can give an even sum is therefore

to find the unit price, we must figure out the cost of one item (in this case one dish towel).   to do this, we divide the total price ($7.92) by the number of items bought (for this problem it is 8, because there are eight dish towels in one pack).  

$7.92/8 = $0.99

therefore, the unit price, or the price of one dish towel, is $0.99.

hope this !

step-by-step explanation:

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