Judithpader123idn
Answered

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how many permutations can be made with all the letters in the word COFFEE? ​

Sagot :

Bonifaciolovely010idn

Answer:

There are 720 permutations BUT 180 "different" permutations

There are 6 letters (ignoring at the moment that there are 2Fs and 2Es). Therefore there are 6! ways that you can order any 6 letters.

The first can be any of 6

The second can be any of 5 (one already first)

The third can be any of 4 (two already first and second)

The 4th can be any of 3

The 5th can be either of 2

The 6th is whatever is left ie 1

Therefore there are 6*5*4*3*2*1 = 6! or 720 different permutations of any 6 letters. If the 2 "Fs" and 2 "Es" can be distinguished, ie they are different sizes or different colours then that is the answer you require 720 permutations.

HOWEVER, if they CANNOT be distinguished and one F looks just like the other F, then for each and every one of the 720 permutations calculated above there will be an IDENTICAL permutation where we just swap one F for the other one. E.g. F(1)COEEF(2) LOOKS exactly the same as F(2)COEEF(1). They both look like FCOEEF. Therefore we must divide the 720 permutations by 2 to allow for the duplicated Fs. 720 / 2 = 360

We must similarly divide these permutations by 2 to allow for the duplicated Es

360 / 2 = 180

"Different" permutations in this example = 6! / (2!*2!) = 720 /(2*2) = 720/4 = 180

There are 180 DIFFERENT permutations

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