How many different words beginning with $O$ and ending with $E$ can be formed with the letters of the word $^{'} O R D I N A T E^{'}$ ?

8!

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6!

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7!

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\frac{7!}{2}

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Solution

The correct option is C $6!$
The first and last letters are fixed i.e. $^{'} O^{'}$ $ξ$ $^{'} E^{'}$ , So we need to rearrange the remaning $6$ letters in $6$ places.
This cab be done in $^{6} P_{6} = 6!$ ways.
Hence, the answer is $6! .$

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