Given the word 'Asasi'. how many ways can three of the letters be chosen and written in a row?

1 Answer
Alan P.
May 20, 2016

#18# ways

Explanation:

Case 1: Two A's are in the choice
If the selection includes 2 A's then there are #3# places the other letter could be placed and #2# choices for the letter to be placed in that location.
#color(white)("XXX")3xx2=6# possibilities.

Case 2: Two S's are in the choice
Similarly, if the selection includes #2# S's there will be
#color(white)("XXX")6# other possibilities.

Case 3: There are no duplicated letters
Since there are #3# different letters in "Asasi"
there would be #3# choices for the first letter,
#2# choices for the second letter,
and only #1# choice for the last leter:
#color(white)("XXX")3xx2xx1=6# more possibilities.

Combined Cases
Since each of the cases above are mutually exclusive and there are no other cases that meet the given requirements,
there are #6+6+6=18# possibilities that meet the given requirements.

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