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?
Number of Four letter words
0
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permutations
combinations
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0Permute the word ACIIC and notice that there are two duplicates (i.e. double C and I) – 2017-02-17
2 Answers
2
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 = $8$
1
If you cannot repeat the letters, you have 6 possible words.
You ask for 4 letters words, but conditional to have P as first and F as last letter. This leaves 2 spaces to fill. You have 5 different letters in PACIFIC, but removing P and F you get only 3. Then is $3*2 =6$
If you can repeat the letters, you still have 2 spaces, and 5 letters, which means $5*5=25$