Question

A number of five digits is formed with the digits $0,1,2,3,4$ without repetitions, the probability that it is a number divisible by $4$ is?

• A. $3/16$
• B. $2/8$
• C. $5/16$
• D. $1/5$

Answer 1

Answer: (C)

$5/16$

$0,1,2,3,4$

Total number of five digit numbers that can be formed are $\underset{\underset{4}{\downarrow }}{-}$ $\underset{4^{\prime }}{----}$

$=4\times 4^{\prime }=4\times 24=96$

For a number to be divisible by $4$ last two digits should be divisible by $4$ .

Last two digits can be $04,12,20,24,32,40=6$

If last rwo digits are $04,20$ or $40$ $\underset{3^{\prime }}{---}$ $\underset{\underset{3}{\downarrow }}{--}$

$=6\times 3=18$

If last two digits are $12,24$ or $32$ $\underset{\underset{2}{\downarrow }}{-}\underset{2^{\prime }}{--}\underset{3}{--}$

$=2\times 2^{\prime }\times 3=12$

Total $18+12=30$ nos.

Probability$=\frac{30}{96}=\frac{10}{32}=\frac{5}{16}$

$\therefore$ Probability$=5/16$ .