A number theory problem by st ramanujan
Number Theory
Level
2
How many integers between 1000 and 9999 have four distinct digits?
3024
4536
6480
6561
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1 solution
For the first digit, there are 9 possible choices, the integers 1-9 inclusive. For the second digit, there are 8 possible choices, integers 0-9 inclusive minus the integer selected for the first digit. For the third digit, 8 choices, for the fourth, 7 choices. The answer is therefore 9 ∗ 9 ∗ 8 ∗ 7 = 4 5 3 6