Answer as a fraction is 1/5040
Answer in decimal form is approximately 0.000198
===========================================================
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.
