You can do that but you have incorrectly calculated the probability that all of the missing stamps are unused.
You have 24 stamps, 10 of which are 'unused'. The probability the first stamp missing is unused is 10/24= 5/12. There are then 23 stamps, 9 of which are unused. The probability the second stamp missing is unused is 9/23. There are then 22 stamps, 8 of which are unused. The probability the third stamp missing is unused is 8/22= 4/11. The probability all three missing stamps are unused is so the probability there is at least one used stamp among the missing stamps is .