Consider the set $A=\{1,2,3,4,5,6\}$ and let B be the power set of A. So the question is: How many one to one functions $f:A\to B$ are there, such that $1 ∉ f(1), 2 ∉ f(2)$? I am having a really hard time with this problem, I spent a few hours giving it a thought but I really don´t have a clue. Thanks!
2026-04-08 15:50:30.1775663430
Discrete math. How many one to one functions satisfy the following property.
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Start with $f(1)$. There are$32$ choices, $16$ of which include $2$ and $16$ that do not. For the ones that include $2$ you have $32$ choices for $f(2)$, for the others $31$. So there are $16(31+32)$ choices for the first two, then $62$ for $f(3)$ and so on