Answer:
24360 combinations
Step-by-step explanation:
The first slot has no limitations. It can be any number from 1-30, therefore, it has 30 options.
The second slot, however, is limited by the number in the first slot. It can be any number from 1-30 except for the number in the first slot. Therefore, it has 29 (= 30 - 1) options.
Finally, the third slot is also limited by the first slot and is also being limited by the second slot. It can be any number from 1-30 except for the numbers in either the first or second slots. Therefore, it has 28 (= 30 - 2) options.
Therefore, the number of combinations is the product of all three slots' options (as multiplication represent the "and" keyword).
[tex]C = 30 \times 29 \times 28 = 24360 \text{ combinations}[/tex]
