365! / ((365-35)! * 365^35)

365!  =  365 x 364 x 363 x ... x 332 x 331 x 330!

(365 - 35)!  =  330!

So:  365! / 330!  =  365 x 364 x 363 x ...x 332 x 331  (because the 330! in the numertor cancels the 330! in the denominator.

You are left with: [ 365 x 364 x 363 x ...x 332 x 331 ] / 365 ^ 35

Which would be:  365/365 x 364/365 x 363/365 x ... x 331/365

Now with patience, your answer will be ...