$\begin{array}{1 1}(A)\;\large\frac{1}{5040}\\(B)\;\large\frac{2}{4035}\\(C)\;\large\frac{3}{5040}\\(D)\;\text{None of these}\end{array} $

- Required probability =$\large\frac{n(E)}{n(S)}$

Step 1:

Given repetition is not allowed.

$\therefore$ First place can be filled in 10 ways.

Second place can be filled in 9 ways.

Third place can be filled in 8 ways

Fourth place can be filled in 7 ways

$\therefore$ Total number of ways =$10\times 9\times 8\times 7$

$\Rightarrow 5040$ ways

Step 2:

Total number of outcomes n(S)=5040

Only one sequence will be right which will open the lock

No of favorable cases n(E)=1

Required probability=$\large\frac{n(E)}{n(S)}$

$\Rightarrow \large\frac{1}{5040}$

Hence (A) is the correct answer.

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