Suppose that 7 people check their coats in a checkroom. If all claim checks are lost and the 7 coats are randomly returned, what is the probability that all the people will get their own coats back?

Work Shown:

We have 7 people. The first person randomly picks a coat, so they have 7 coats to choose from. We'll have 7-1 = 6 coats left. Then person #2 is up to pick randomly from those 6 coats to have 6-1 = 5 coats left over for person #3. This keeps going til person #7 has no choice but to take what is left over.

The countdown of values 7,6,5,4,3,2,1 is multiplied out to get

7*6*5*4*3*2*1 = 5040

There are 5040 permutations possible. Order matters.

There is only one permutation in which everyone gets their coat back, and this is out of 5040 possibilities.

So that's where 1/5040 comes from.

Use your calculator to find that 1/5040 = 0.0001984 approximately.

answer by yourhope:

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step-by-step explanation: