Question

Let $A=\{1,2,3,4,5,6\}$and $f:A\to A$ be a bijection. What is the probability that $fof=id,i.e.,f$ is its own inverse?

• A. $\frac{19}{180}$
• B. $\frac{13}{48}$
• C. $\frac{1}{720}$
• D. $\frac{5}{16}$

Answer 1

The correct option is A $\frac{19}{180}$

Set $A=[1,2,3,4,5,6]$

Shown that $f:A\to A$ is a bijection.

i.e, $f\left(x\right)=y.$

$=\frac{\left[\right(1+2+3+4+5+6)-2]4}{6!}$

$=\frac{19\times 4}{720}$

$=\frac{19}{180}.$

Hence, the answer is $\frac{19}{180}.$