From the digits 1,2 ,3 ,4 and 5, 4-digit numbers can be formed. There are permutations of 5 different things taken 4 at a time. Thus, number of 4 digit numbers
\( ^5P_4=\dfrac{5!}{(5-4)!}=\dfrac{5!}{1!}\)
= 1×2×3×4×5=120
Out of 1, 2, 3, 4, 5, we know that even numbers end either by 2 or 4. Thus, ways in which units place can be filled is 2. Since, repetition is not allowed, units place is already occupied by a digit and remaining vacant places can be filled by remaining 4 digits. Thus, number of ways in which remaining places can be filled =
= \( ^4P_3=\dfrac{4!}{(4-3)!}=\dfrac{4!}{1!}\)
= 4×3×2×1= 24
Therefore, by multiplication principle, number of even numbers \( 24\times 2=48\)
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