The probability that a randomly chosen one-one function from the set $\left\{a,b,c,\left.d\right\}\right.$to the set $\left\{1,2,3,\left.4,5\right\}\right.$satisfied $f\left(a\right)+2f\left(b\right)-f\left(c\right)=f\left(d\right)$ is

Here no. of element in sample

$n\left(s\right)=5\times 4\times 3\times 2=120$

None for favourable cases

$\therefore$No. of favourable cases

$n\left(A\right)=2!\times 3=6$

$\therefore P\left(A\right)=\frac{No.offavourablecases}{Totalno.ofcases}$

$\therefore P\left(A\right)=\frac{1}{20}$