We got a bunch of balls numbered 1 to n. And we got a bunch of bowls numbered also 1 to n. What is the chance of ball x hitting bowl x after dropping each ball randomly in a bowl one by one? The answer involves saying 1/n after going (n-1)!/n! and I wonder, what is the full logic behind it? I think I can get the denominator as a collection of all the shuffling results, but what is the exact logic that leads to the numerator being (n-1)!?