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Home  >>  CBSE XI  >>  Math  >>  Permutations and Combinations
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Using the digits 1,2,3,4,5,6,7,a number of 4 different digit is formed. Find How many numbers are exactly divisible by 2

$\begin{array}{1 1}(A)\;360\\(B)\;125\\(C)\;150\\(D)\;175\end{array} $

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We have to look for no which ends with 2,4 or 6
The last digit has to end with 2,4,6
The other three digit no.can be formed =1,3,4,5,6,7 as the last digit is 2
Hence the no. of ways =$6P_3$
$\Rightarrow \large\frac{6!}{3!}$
$\Rightarrow \large\frac{6\times 5\times 4\times 3!}{3!}$
$\Rightarrow 120$
$\therefore$ Applying the same
We get the same for numbers ending with 4 or 6
Thus the total no of ways =$120\times 3$
$\Rightarrow 360$
Hence (A) is the correct answer.
answered May 19, 2014 by sreemathi.v

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