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Permutation under Restriction

How many four...

Question

How many four letter words with or without meaning, can be formed out of the letters of the word $^{'} L O G A R I T H M S^{'}$ if repetition is not allowed?

A

40

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B

400

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C

5040

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D

2520

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Solution

The correct option is B $5040$
Four letter word has to be selected from the word $L O G A R I T H M S$
which can be done in $^{10} C_{4}$ ways and they can be arranged in $4!$ ways.
$^{10} C_{4} \times 4! = 5040$

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