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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 (c) How many numbers are exactly divisible by 25

$\begin{array}{1 1}(A)\;40\\(B)\;25\\(C)\;50\\(D)\;75\end{array} $

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The no.divisible by 25 should end with 5
Thus the last two digit should be 25 or 75 for other 2 digit no. we have =$5P_2$
$\Rightarrow \large\frac{5!}{3!}$
$\Rightarrow \large\frac{5\times 4\times 3!}{3!}$
$\Rightarrow 20$
Hence if the last two digit is 75
The no. of ways will be 20
Thus the total no. of way =20+20
$\Rightarrow 40$
Hence (A) is the correct answer.
answered May 19, 2014 by sreemathi.v

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