That's a lot more than the number of possible combinations you can make with 12 words, which is 12! = 479001600. Brute-forcing a seed phrase out of 12 correct but randomized words is not impossible.
Although using 12! permutations is correct for estimating the number of ways to arrange 12 words, it's not an accurate estimate for the number of valid BIP39 seed phrases you can generate from them. There are two points one have to take into account: 1) in the valid BIP39 seed phrase the last word encodes the checksum 2) seed phrase may contain duplicates. Thus the actual number of valid seed phrases you can build from the given set of 12 BIP39 words depends on the specific words and is hard to estimate in general case.