How many numbers can you get by multiplying two or more distinct members of the set $\{1,2,3,5,11\}$ together?
Note that, because two or more members can be multiplied, multiplying by $1$ will only make a difference if it is one of two numbers. Thus, multiplying by $1$ adds four potential numbers.

Now, we only need to consider the number of combinations that can be made from $2$, $3$, $5$, and $11$.

Choosing two from this set offers six possiblities: $2 \cdot 3$, $2 \cdot 5$, $2 \cdot 11$, $3 \cdot 5$, $3 \cdot 11$, and $5 \cdot 11$.

Choosing three offers four possibilities: $2 \cdot 3 \cdot 5$, $2 \cdot 3 \cdot 11$, $2 \cdot 5 \cdot 11$, and $3 \cdot 5 \cdot 11$.

Finally, there is one possibility with four chosen: $2 \cdot 3 \cdot 5 \cdot 11$. Thus, there are $4 + 6 + 4 + 1 = \boxed{15}$.
15
Level 5
Prealgebra
Problem: How many numbers can you get by multiplying two or more distinct members of the set $\{1,2,3,5,11\}$ together?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To determine how many distinct products can be formed by multiplying two or more distinct members of the set {1, 2, 3, 5, 11}, we first identify the distinct combinations of these numbers. The set contains five elements, and we can choose any combination of two or more elements to form a product.

We start by calculating the products of all combinations of two elements. The pairs are:
- 2 * 3 = 6
- 2 * 5 = 10
- 2 * 11 = 22
- 3 * 5 = 15
- 3 * 11 = 33
- 5 * 11 = 55

Next, we calculate the products of all combinations of three elements:
- 2 * 3 * 5 = 30
- 2 * 3 * 11 = 66
- 2 * 5 * 11 = 110
- 3 * 5 * 11 = 165

Then, we consider the products of all combinations of four elements:
- 2 * 3 * 5 * 11 = 330

Finally, we consider the product of all five elements:
- 1 * 2 * 3 * 5 * 11 = 330

Now, we compile all the distinct products obtained from these combinations:
- From two elements: 6, 10, 15, 22, 30, 33, 55
- From three elements: 30, 66, 110, 165
- From four elements: 330
- From five elements: 330

Next, we list all distinct products:
- 6, 10, 15, 22, 30, 33, 55, 66, 110, 165, 330

We count these distinct products. The total number of unique products is 15. Thus, the final answer is 15.<|END_OF_LATENT|> The final answer is $15$.