Question

$i$ five digit number is formed by the digits $1,2,3,4,5$ without repetition. Find the probability that the number formed is divisible by $4$.

• A. $\frac{1}{20}$
• B. $\frac{1}{30}$
• C. $\frac{1}{5}$
• D. $\frac{4}{5}$

Answer 1

Answer: (C)

$\frac{1}{5}$

Total no. of five digit numbers $=5!=120$.
Now a number will be divisible by $4$ if the last two digits are divisible by $4$ if the last two digits are divisible by $4$. Therefore the last two digits can be $12,24,32,52,$ that is, they can be filled in $4$ ways.
Corresponding to each of these ways there are $3!=6$ ways of filling the remaining three places.
Hence $m=$ favourable no. of ways $=4\times 6=24$
$\therefore$ The required probability $=\frac{24}{120}=\frac{1}{5}$