Q78 / 160 · TS EAMCET 2016 · Mathematics
A five digit number is formed by the digits 1 , $2,3,4,5$ with no digit being repeated. The probability that the number is divisible by 4 , is
- Correct answerA$\frac{1}{5}$
- B$\frac{2}{5}$
- C$\frac{3}{5}$
- D$\frac{4}{5}$
Solution
Number is divisible by 4 , if last two digits are 12, 24, 32 and 52.
Remaining 3 place will be filled by 3 ! ways.
$$
\begin{aligned}
\therefore \quad \text { Favourable outcomes } & =3 ! \times 4 \\
\text { Hence, required probability } & =\frac{3 ! \times 4}{5 !} \\
& =\frac{3 ! \times 4}{5 \times 4 \times 3 !}=\frac{1}{5}
\end{aligned}
$$
Hence, the correct answer is option: 'A'.