The number of four digited numbers formed by 2, 4, 5, 7, 8 divisible by 4 (when repetition is not allowed ) is

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The number of four digited numbers formed by 2, 4, 5, 7, 8 divisible by 4 (when repetition is not allowed ) is

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Detailed Solution

A number is divisible by 4 if last 2 digits of the number is divisible by 4.

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Given digits 2, 4, 5, 7, 8 to make the number divisible by 4 the last 2 places can be occupied by 24, 28, 48, 52, 72, 84 (6 ways).

Remaining 2 places can be filled by remaining 3 digits in $^{3} P_{2}$ ways.

$∴$ Required number of numbers $=^{3} P_{2} \times 6 = 36$

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