Probability of Seven (Distinct) car accidents occurred on the same day
Solution 1:
There are seven days and seven accidents (which are distinguishabla from one another), so the number of possible outcomes is $7^7$. However, only seven of them fulfil our criteria: all accidents on Monday, all on Tuesday, ..., all on Saturday. So the answer is $1/7^6$.
Solution 2:
The probability that $1$ accident occurs on a given day is $\frac17$
The probability that $7$ accidents occur on a given day is $(\frac17)^7$
The probability that $7$ accidents occur on the same day is $(\frac17)^7\cdot7$