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# Can I have help please?

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

May 10, 2021

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Use casework. First try finding the possiblities with only multiplying 2 numbers, and then the possibilities with multiplying 3 numbers, etc.

Using 2 numbers: $$2\cdot3, 2 \cdot 5, 2 \cdot 11, 3 \cdot 5, 3 \cdot 11, 5 \cdot 11.$$

Using 3 numbers: $$2 \cdot 3 \cdot 5, 2 \cdot 3 \cdot 11, 2 \cdot 5 \cdot 11, 3 \cdot 5 \cdot 11.$$

Using 4 numbers: $$2 \cdot 3 \cdot 5 \cdot 11.$$

So we have a total of $$6+4+4+1=\boxed{15}$$

May 10, 2021