Question

Using the digits $1,2,3,4$ all t a time digit number are formed.What is the probability that number formed is even ?

Answer 1

For the number formed to be even the once place should have $2$ or $4$

as we take $2$ in once place then the total number formed is given as $3!$ (by the arrangement of $1,3,4$ in remaining three place)

and we take $4$ in once place, the total number of even number formed is given as $3!$

therefore total number of even number formed $=3!+3!=12$

and total number formed by taking all the four numbers is given as $4!=24$

$\therefore p\left(\frac{totalnumberofevennumber}{totalnumberisformed}\right)=\frac{12}{24}=\frac{1}{2}$