How many different four letter words can be formed (the words need not be meaningful) using the letters of the word PACIFIC such that the first letter is P and the last letter is F?
[Math] Number of Four letter words
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combinationspermutations
How many different four letter words can be formed (the words need not be meaningful) using the letters of the word PACIFIC such that the first letter is P and the last letter is F?
Best Answer
P _ _ F
If repetition is allowed
Letters available to fill the space are P, A, C, I and F. (Doppelgangers of C and I don't matter)
Total number of arrangements = $5 \times5=25$
If repetition is NOT allowed
Letters available for arrangement are A,C,C,I and I. (P and F are already used)
First, let's consider only A, C and I.
Number of arrangements = $3\times2=6$
And there are other 2 cases are where letters 'C' and 'I' repeat twice in each respective case.
So, total number of arrangements = $8$