Count the bijections from A to B, given that |A|=|B|= n.

homework hint: No proof required. Count the bijections from {1,2} to {1,2}, then count the bijections from {1,2,3} to {1,2,3}, etc. When you are confident you know the formula for the number of bijections from {1,2,...,n} to {1,2,...n}, then write it down.

My question: what does counting bijections mean? I thought a function was either a bijection or not =|