Final answer:
There are 224 different gift packages possible when selecting 3 round candles from 4 types and 3 square candles from 8 types.
Step-by-step explanation:
The question asks how many different gift sets can be made from 4 types of round candles and 8 types of square candles, with each gift set consisting of 3 round and 3 square candles. To determine this, we utilize combinations. The number of ways to select 3 round candles from 4 is a combination problem, which is calculated as C(4,3). Similarly, the number of ways to select 3 square candles from 8 is C(8,3).
The formula for a combination is C(n,k) = n! / (k!(n - k)!), where n is the number of items to pick from, k is how many to pick, and "!" stands for factorial. By calculating the combinations for both round and square candles and then multiplying the two results together, we obtain the total number of different gift sets possible.
For round candles, C(4,3) = 4! / (3! * (4 - 3)!) = 4. For square candles, C(8,3) = 8! / (3! * (8 - 3)!) = 56. The total number of different gift packages is 4 * 56 = 224.
Thus, there are 224 different gift packages possible with the given types and quantities of candles.