Which equation is right for my probability question?

Question

For the combination question I have
25!/20!5! my book says that to answer this I do 25*24*24*22*21*20!/5*4*3*2*1*20!=53,130

My professor says that I should do it
25*24*23*22*21!/5*4*3*2*1=53,130

Their both the same answer but which is correct?

Answer 1

Your professor is right. The 20! cancel each other out, leaving you with 25*24*23*22*21/5*4*3*2*1.

Answer 2

The answer is 25*24*23*22*21/5*4*3*2*1 (no factorial on the 21). That's because 25! / 20! = 25*24*23*22*21*20! / 20! and the 20!'s cancel out.