Question

A six digit number is formed with the digits $0,1,2,3,4,7$ without repetition. Then the probability that it is divisible by $4$, is

• A. $\frac{12}{25}$
• B. $\frac{6}{25}$
• C. $\frac{3}{25}$
• D. $\frac{21}{100}$

Answer 1

Answer: (B)

If the $6$ digit number is to be divisible by $4$,
the last two digits have to be one of the following pairs
$04,12,20,24,32,40,72$.
$\therefore$ The number of favourable ways
$\lfloor 4+3\cdot 3\cdot 2\cdot 1+\lfloor 4+3\cdot 3\cdot 2\cdot 1+3\cdot 3\cdot 2\cdot 1$
$+\lfloor 4+3\cdot 3\cdot 2\cdot 1=144$.
Total number of numbers that can be formed
$=6!-5!=5!(6-1)=600$
Hence the probability $=\frac{144}{600}$
$=\frac{6}{25}$.