This question used to bother me too when I was in 11th and studied Permutation & Combination for the first time.

See, that's how my Maths teacher explained to me :

In mathematics, all theories are governed by a set of rules and patterns that must be obeyed throughout the …

Factorial of n is n! and the value of n! is n!=n×(n−1)×(n−2)×………×1

The value of n! from the above can be also written as n×(n−1)! ⇒n!=n×(n−1)!

Considering the value of n equal to 1, ⇒1!=1!×(1−1)! ⇒1!=1!×(0)! For above condition to be true The value of 0! must be equal to …