Question

A number of five digits is formed with the digits 0, 1, 2, 3, 4 without repetition. The probability that it is a number 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 last two digits are 04, 40, 24, 32, 20, 12.
$\therefore$ Total number of favourable ways
= 3! + 3! + 4 + 4 + 3! + 4 = 30
And total numbers that can be formed
= 5! – 4! = 4! (5 – 1) = 96
$\therefore$ P (number divisible by 4) =$\frac{30}{96}=\frac{5}{16}$