How many numbers can you get by multiplying two or more distinct members of the set $\{1,2,3,5,11\}$ together?

In multiplication, order does not matter. so we use combinations for this question instead of permutations.in the set  , there are 5 numbers.multiplying two numbers together: out of 5 numbers, how many ways are there to choose two numbers (to multiply with each other)? multiplying three numbers together: out of 5 numbers, how many ways to choose three numbers? but then if 1 is chosen, then there will be duplicates from the number of ways to multiply two numbers together.if the first number is 1: 1 _ _ to fill those slots, there are 4 digits in the set that are not one, and we need to choose two. so the number of duplicates is  so  multiplying four numbers together: out of 5 numbers, how many ways to choose four numbers? , but there  will be duplicates from the number of ways to  multiply two numbers together.if the first number is 1: 1 _ _ _to fill those slots,  there are 4 digits in the set that are not one, and we need to choose two. so the number of duplicates is  multiplying five numbers together: out of 5 numbers, how many ways to choose five numbers? but this is just a duplicate of the last case. if one is one of the numbers, then multiplying from one is essentially like one of the ways to multiply four numbers together, namely 2, 3, 5, 11. so ignore this casetotal: 10 + 4 + 1 = 15

Ais the correct answer