If 4 people have the same 7 shirts, what is the chance that they will wear the same shirt on one day

[math_celebrity]

If 4 people have the same 7 shirts, what is the chance that they will wear the same shirt on one day?

1. For each person, the probability they all wear the first shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256
2. For each person, the probability they all wear the second shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256
3. For each person, the probability they all wear the third shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256
4. For each person, the probability they all wear the fourth shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256
5. For each person, the probability they all wear the fifth shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256
6. For each person, the probability they all wear the sixth shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256
7. For each person, the probability they all wear the seventh shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256

Now, we add up all those probabilities to get our answer, since any of the 7 scenarios above meets the criteria:
(1 + 1 + 1 + 1 + 1 + 1 + 1)/256
7/256