A number lock on a suitcase has 3 wheels,each | vedclass

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Question

(A) The lock has $3$ wheels,and each wheel can be set to any of the $10$ digits ($0$ through $9$).Since the sequence of $3$ digits must have no repeat

Vedclass · Accepted Answer

$720$

Vedclass · Answer

(A) The lock has $3$ wheels,and each wheel can be set to any of the $10$ digits ($0$ through $9$).Since the sequence of $3$ digits must have no repeats,we are looking for the number of permutations of $10$ distinct items taken $3$ at a time.For the first wheel,there are $10$ possible choices.For the second wheel,since repetition is not allowed,there are $9$ remaining choices.For the third wheel,there are $8$ remaining choices.Therefore,the total number of possible sequences is $10 	imes 9 	imes 8 = 720$.

$A$ number lock on a suitcase has $3$ wheels,each labelled with $10$ digits from $0$ to $9$. If opening the lock requires a particular sequence of $3$ digits with no repeats,how many such sequences are possible?

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