A four digit number is formed by using the digits 1, 2, 4 and 5 with no repetition. The probability that the number is divisible by 5, is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1/4
Using all four digits without repetition, the number of four digit numbers is
\( \displaystyle 4!=24 \)
A number is divisible by 5 only if its last digit is 0 or 5; here the last digit must be 5. The other three digits can be arranged in the first three places in
\( \displaystyle 3!=6\ \text{ways} \)
\( \displaystyle P=\frac{6}{24}=\frac{1}{4} \)
Shortcut: Each of the four digits is equally likely to be in the units place, so the probability that 5 is there is 1/4.