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A suitcase lock has 4 dials with the digits 0, 1, 2,..., 9 on each. How many different settings are possible if all four digits have to be different and the combination must be greater than 7000? 

 Jul 2, 2022
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There are:

10 P 4 ==5040 permutations

 

Since each permutations begins with one of the 10 digits, we therefore have:

 

5040 / 10 ==504 permutations beginning with one of the 10 digits.

 

Since we want all permutations >7000, we therefore should have:

 

504 x 3 ==1,512 permutations > 7000.

 Jul 2, 2022

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