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Permutation: n Different Things Taken r at a Time

How many four...

Question

How many four letter words can be formed from the letters of the word "LOGARITHMS", if repetation is not allowed ?

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Solution

The word “ LOGARITHMS” has 10 different letters and we have to form words using any 4 letters from the 10 given letters.
Therefore,
Total no. of words that can be formed
= $10 P 4$ = $\frac{10!}{(10 - 4)!}$ = 5040

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