Question

A five digit number is formed with digits 0. 1. 2. 3. 4 without repetition. A number is selected at random, then the probability that it is divisible by 4 is

• A. $\frac{1}{3}$
• B. $\frac{5}{16}$
• C. $\frac{1}{4}$
• D. $\frac{4}{15}$

Answer 1

The correct option is B $\frac{5}{16}$

The number formed is divisible by 4 if the last two digits are 04,40,34,32,20,12.
Therefore total number of favorable ways = 3! + 3! +4 + 4+ 3! + 4 = 30 (This is the sum of number of ways in which the first two digits can be formed)
Total numbers that can be formed = 5! – 4! = 96 ( Number of ways of arranging 5 digits - Number of ways in which zero comes as the first digit)
Therefore required probability $=\frac{30}{96}=\frac{5}{16}.$