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
Show Hint
- $\dfrac{1}{5}$
- $\dfrac{5}{6}$
- $\dfrac{4}{5}$
- $\dfrac{1}{6}$
The Correct Option is A
Solution and Explanation
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 = $\dfrac{24}{120} = \dfrac{1}{5}$
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