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)!?

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)!?

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