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

$\begin{array}{1 1}(A)\;48\\(B)\;52\\(C)\;54\\(D)\;56\end{array}$

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## 1 Answer

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• $nP_r=\large\frac{n!}{(n-r)!}$
Out of 5 digits 4 digit numbers are to be formed
Such numbers are $5P_4$
$5P_4=\large\frac{5!}{(5-4)!}$
$\;\;\;\;\;\;\;=\large\frac{5!}{1!}$
$\;\;\;\;\;\;\;=5\times 4\times 3\times 2$
$\;\;\;\;\;\;\;=120$
When 2 is at unit's place ,then remaining three places are filled in $4P_3$ ways
$4P_3=\large\frac{4!}{(4-3)!}$
$\qquad=4\times 3\times 2$
$\qquad=24$
When 4 is at units place,then 4 digit numbers are again =24
$\therefore$ Even 4 digit numbers =$2\times 24$
$\Rightarrow 48$
Hence (D) is the correct answer.
answered May 13, 2014

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