Find the number of $4$-digit numbers that can be formed using $1,2,3,4,5$ if no digit is repeated. How many of these will be even?

Question

I'm unable to solve this question. Please help. I have no idea. The given answers are $120$ and $48$. I got $120$ but not $48$. This is how I got $120$.

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No repetition allowed, so $5\times4\times3\times2=120$ ways.

Answer 1

The ones digit has to be 2 or 4 (as it has to be even). That makes 2 choices.
These 2 choices are chosen among 5 other choices.

Therefore, the answer should be $\frac{2}{5}\times5\times4\times3\times2 = 48$

Answer 2

Its easy suppose a four digit number which is to be made from digits $1,2,3,4,5$. In thousandth place possible number adjusted is $5$. In hundredth place possible number adjusted is $4$. Repetition is not allowed. In tens place possible number adjusted is $3$. In ones place possible number adjusted is $2$. Total no is $5×4×3×2=120$. For even number Even number has unit digit $2$ or $4$ So in ones place possible number adjusted is $2$. In thousandth place possible number adjusted is $4$. In hundredth place possible number adjusted is $3$. In tens place possible number adjusted is $2$. Total even no. is $2×4×3×2=48$.