That's correct. It's very hard to imagine it being that big but if you started listing them out in a sequential order, starting with the smallest possible combination and build from there, you will see how much room there is to have slight deviations.

Say 0123456789 then 0123456798 then 0123456879 then 0123456897 then 0123456978 then 0123456987

This is barely scraping into starting with 0 as the first number and grows exponentially in possibilities the further into the base number you change.

Binary is somewhat similar and can help you appreciate the scale of it all

start with

0000000001

then

0000000010

(In binary you can only count using 1's and 0's, so the first number is 1 and the second is 2)

You can see we already moved up one space by increasing by just one number. But the further in you go, the quicker it grows.

for 3 it would be

0000000011

(we didn't move up a place)

then

0000000100 0000000101 0000000111

0000001000 0000001001 0000001010 0000001011 0000001100 0000001101 0000001110 0000001111

You can see at this rate, that it truly is exponential. Still, it's hard to accept that 10! is so large and applicable to combinatorics, but I hope this somewhat helps you. And if you ever doubt it, start with lists like this, and you'll see that it's a lot bigger than you could have initially imagined