(A) The number lock has $4$ wheels,each labelled with $10$ digits,i.e.,from $0$ to $9$.The total number of ways to choose and arrange $4$ distinct dig

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(A) The number lock has $4$ wheels,each labelled with $10$ digits,i.e.,from $0$ to $9$.The total number of ways to choose and arrange $4$ distinct digits out of $10$ is given by the permutation formula $P(n, r) = \frac{n!}{(n-r)!}$.Here,$n = 10$ and $r = 4$.Total possible sequences $= P(10, 4) = \frac{10!}{(10-4)!} = \frac{10 \times 9 \times 8 \times 7 \times 6!}{6!} = 10 \times 9 \times 8 \times 7 = 5040$.Since there is only $1$ correct sequence to open the suitcase,the probability is $\frac{1}{5040}$.

Class 11 Mathematics Permutation and Combination Definition of permutation, Number of permutations with or without repetition, Conditional permutations

Difficult

The number lock of a suitcase has $4$ wheels,each labelled with ten digits,i.e.,from $0$ to $9$. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?

A
$\frac{1}{5040}$
B
$\frac{1}{2520}$
C
$\frac{1}{10000}$
D
$\frac{1}{5000}$

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Permutation and Combination

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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The number lock of a suitcase has $4$ wheels,each labelled with ten digits,i.e.,from $0$ to $9$. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?

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