Different ways to split 8 people into at least two non-empty groups

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In how many different ways can you split 8 people into at least two non-empty groups?

My attempt:
Since Bell number of 8 elements set is 4140 and we don't need whole set in one partition, is the answer: 4140 - 1?

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Looks good to me. As long as you have the Bell numbers available, and aren't expected to derive the 8th Bell number yourself.