Question

Five-digit numbers are formed using digits 1,2,3,4,5 without repetition. Then the probability that the randomly chosen number is divisible by 4 is

• A. $\dfrac{1}{5}$
• B. $\dfrac{5}{6}$
• C. $\dfrac{4}{5}$
• D. $\dfrac{1}{6}$

Hint:

For divisibility by 4, check last two digits; apply factorial counting accordingly.

Answer 1

The Correct Option is A

Total 5-digit numbers without repetition using digits 1–5 = $5! = 120$
For divisibility by 4, check last two digits. Number is divisible by 4 if last two digits form number divisible by 4
Among all permutations, find those where last two digits form 2-digit numbers divisible by 4
From digits 1–5, valid 2-digit endings divisible by 4 without repetition are: 12, 24, 32, 52, 44 (invalid due to repetition)
Valid endings = 12, 24, 32, 52
Each such ending can be paired with the remaining 3 digits in $3! = 6$ ways
So favorable = $4 \cdot 6 = 24$
Probability = $\dfrac{24}{120} = \dfrac{1}{5}$