The digits 1, 3, 5, 6 and 8 are arranged in a random order to make a five-digit number, each digit being used exactly once. What is the probability that the number made is a multiple of 4?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\frac{1}{5}\)
A number is a multiple of 4 when the number formed by its last two digits is a multiple of 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 among 1, 3, 5, 6, 8 that are multiples of 4: 16, 36, 56, 68
For each ending, the other 3 digits fill the first three places in \(3!=6\) ways
Multiples of 4 \(=4\times6=24\)
Probability \(\displaystyle =\frac{24}{120}=\frac{1}{5}\)