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# Probability Question

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Ellen has five different jobs to be done. She assigns each of the five jobs to one of her four kids so that each kid will have at least one job. How many ways can Ellen assign the jobs?

May 12, 2020

#1
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I am not completely sure of this answer.

Both the kids and the jobs are distinct.

Therefore, we have $$5 \cdot 4 \cdot 3 \cdot 2$$ ways of ordering the jobs since each kid must have at least one job.

There are $$5$$ jobs available for the first kid, $$4$$ for the next, and so on.

Now we have assigned each kid a job and we have one job left.

Thus, we have $$4$$ choices.

$$5 \cdot 4 \cdot 3 \cdot 2 \cdot 4 = \boxed{480}$$

May 12, 2020
#2
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