How many different non-trivial factorisations does

3 × 5 × 7 × 11 × 13 × 17 × 19 × 23 × 29 × 31 = 100280245065.

have?

Since there are 10 primes, i thought the answer would be

sum_(i=0)^n {10 \choose i} - 1 = 2^10 - 1

but i am a little bit unsure if i am not counting anything double.