Probability of Seven (Distinct) car accidents occurred on the same day Seven (Distinct) car accidents occurred in a week. What is probability that they all occurred on the same day?
My Solution:

All 7 accident occurs in 1 day in $\binom{7}{1}$ ways
All 7 accident occurs in 2 days in $\binom{7}{2}$ ways
All 7 accident occurs in 3 days in $\binom{7}{3}$ ways
All 7 accident occurs in 4 days in $\binom{7}{4}$ ways
All 7 accident occurs in 5 days in $\binom{7}{5}$ ways
All 7 accident occurs in 6 days in $\binom{7}{6}$ ways
All 7 accident occurs in 7 days in $\binom{7}{7}$ ways

Hence P(They all occurred on the Same day)$=\frac{\binom{7}{1}}{\binom{7}{1}+\binom{7}{2}+\binom{7}{3}+\binom{7}{4}+\binom{7}{5}+\binom{7}{6}+\binom{7}{7}}$
$=\frac{7}{2^7}$
Is my analysis correct or I've assumed something wrong

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 $1/7^6$.
