A five-digit number is formed at random using each of the digits 1, 2, 3, 4 and 5 once, without repetition. What is the probability that the number is divisible by 4?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\frac{1}{5}\)
A number is divisible by 4 when the number formed by its last two digits is divisible by 4. So count the possible endings first, then fill the other three places.
All five-digit numbers \(=5!=120\)
Two-digit endings from different digits 1 to 5 that are multiples of 4: 12, 24, 32, 52
For each ending, the other 3 digits fill the first three places in \(3!=6\) ways
Numbers divisible by 4 \(=4\times6=24\)
Probability \(\displaystyle =\frac{24}{120}=\frac{1}{5}\)