Question

A 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. $31/120$
• B. $1/2$
• C. $1/5$
• D. $1/3$

Answer 1

Answer: (C)

$1/5$

Total number of five-digit number $=5!=120$
Now a number is divisible by $4$ if the last two digits (i.e digits at unit and 10 place) are divisible by $4$.
Therefore, the last two digits can be $12,24,32,52$ and thus there are four ways.
Corresponding to each of these, there are $3!=6$ ways of filling the remaining three digits
Hence, the total number of favorable ways $=6\times 4=24$
Therefore the required probability $=\frac{24}{120}=\frac{1}{5}$