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#### Pranav

##### Well-known member

- Nov 4, 2013

- 428

**Problem:**

Let $f:\{1,2,3,4,5\}\rightarrow \{1,2,3,4,5\}$, then the number of functions which are into and satisfy $f(i)=i$ for at least one $i=1,2,3,4,5$ are

A)435

B)2121

C)2025

D)None of these

**Attempt:**

Looking at the opposite case i.e where $f(i)=i$ for at least one of the given i's is not satisfied, I can find the number of derangements but I am not sure if it helps. I need a few hints to begin with. My mind goes blank on these combinatorics problems.

Any help is appreciated. Thanks!