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?
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.