Tessellate S.T.E.M.S. (2019) - Computer Science - School - Set 3 - Objective Problem 4

Probability Level 3

The number of functions $f:\{1,2,\ldots, n\}\rightarrow \{1,2,\ldots,n\}$ such that $f(x)\neq x$ are:

This problem is a part of Tessellate S.T.E.M.S (2019)

n^n

n!

(n-1)^n

n^n-1

n^{n-1}

1 solution

Parth Sankhe
Nov 13, 2018

Each element is the domain will have a choice to become anything in the co-domain through the function, except itself. Therefore each of the $n$ elements in the domain will have $n-1$ choices. Thus the answer = $(n-1)^n$

Tessellate S.T.E.M.S. (2019) - Computer Science - School - Set 3 - Objective Problem 4

1 solution

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