Factorial

$n!$

most basic use is to count the possible distinct sequences – the (repeatable) permutations – of $n$ distinct objects

• "there are $n!$ different ways of arranging $n$ distinct objects into a sequence."
• ex. we have a square, a triangle and a circle and we want to know how many different combinations of order we can make ([triangle, circle, square], [circle, triangle, square] etc.)
  • Here, there are $3!$ combinations, or 6.

A factorial is a multiple of all values less than the factorial value

• ex. 240 ($5!$) is evenly divisible by 5, 4, 3, 2 and 1

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• Permutation