[Math] Number of Four letter words

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 = $8$