The number lock of a suitcase has 4 wheels,ea | vedclass

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Question

(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

Vedclass · Accepted Answer

$\frac{1}{5040}$

Vedclass · Answer

(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 $= P(10, 4) = \frac{10!}{(10-4)!} = \frac{10 	imes 9 	imes 8 	imes 7 	imes 6!}{6!} = 10 	imes 9 	imes 8 	imes 7 = 5040$.Since there is only $1$ correct sequence to open the suitcase,the probability is $\frac{1}{5040}$.

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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