How Many 3-Letter Words With Or Without Meaning, Can Be Formed Out Of The Letters Of The Word "Logariths", If Repitition Of Letters Is Not Allowed?

How many 3-letter words with or without meaning, can be formed out of the letters of the word "LOGARITHS", if repitition of letters is not allowed?

Answer:

504

Computation:

Applying permutation to determine the number of all possible three-letter words with or without meaning that can be formed out of the letters in the word "LOGARITHS" without repetition.

^{n}P_r=\frac{n!}{(n-r)!}\\\\^{9}P_3=\frac{9!}{(9-3)!}=\frac{9*8*7*6*5*4*3*2*1}{6!}=\frac{362,880}{6*5*4*3*2*1}=\frac{362,880}{720}=504


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