Combinatorial Exploration

Given a known number of unique items, how many ways could we arrange them in a row?

Create a function that takes an integer n and returns the number of digits of the number of possible permutations for n unique items. For instance, 5 unique items could be arranged in 120 unique ways. 120 has 3 digits, hence the integer 3 is returned.

Examples

no_perms_digits(0) ➞ 1

no_perms_digits(1) ➞ 1

no_perms_digits(5) ➞ 3

no_perms_digits(8) ➞ 5

Notes

This challenge requires some understanding of combinatorics.