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How many words can be made from the letters of the word MONDAY assuming that no letter is repeated if 4 letters are used at a time

$\begin{array}{1 1}(A)\;360\\(B)\;325\\(C)\;350\\(D)\;175\end{array} $

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Total no of letters =6
No of letters used at a time =4
No of ways =$6C_4$
$\Rightarrow \large\frac{6!}{4!2!}$
$\Rightarrow \large\frac{6\times 5\times 4!}{2\times 4!}$
$\Rightarrow 15$
No of ways of using 4 letters =4!
$\Rightarrow 4\times 3\times 2$
$\Rightarrow 24$
The total no of ways =$15\times 24$
$\Rightarrow 360$
Hence (A) is the correct answer.
answered May 19, 2014 by sreemathi.v

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