Acombination lock has 5 different numbers. if each number can only be used once, how many different combinations are possible?

Hello,

The first digit may be 0,1,2..,9 thus 10 possibilities
The second digit may be 0,1,2,3...,9 but not equal to the first thus 9 possibilities
The 3th digit may be 0,1,2..,9 but not the first and not the 2th =>8 possibiliteis
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In  Total, 10*9*8*7*6 combinations.