Using {1,2,3,4,5} four digited numbers are formed without repetition at random. The probability that the number is divisible by 4 is

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$\frac{3}{5}$

$\frac{1}{5}$

$\frac{4}{5}$

$\frac{2}{5}$

answer is A.

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Detailed Solution

$\begin{array}{l} n (S) = {}^{5}P_{4} = 120 \\ E = Divisible by 4 \\ L a s t t w o p l a c e s c a n b e f i l l e d i n u \sin g \{12, 24, 32, 52\} \\ n (E) = {}^{3}P_{2} \times 4 = 24 \\ ∴ P (E) = \frac{24}{120} = \frac{1}{5} \end{array}$

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