a person wrote 6 letters and there are 4 post offices in a city, in how many ways he can post the letters? (permutations)
Answers
clearly,. he can post the first letter in any of the 4 post office. similarly the 2nd to 6th letters can also be posted in any of the four post offices.
so the number of ways is 4*4*4*4*4*4 = 4^6 ways.
(If you think this way that letters can be posted in the first post office in 6 ways and then in next post office in 5 ways and then four and three and thus total number of ways is 6*5*4*3 = 360. There is a fallacy in this way. this method has assumption that all atleast one letter will be posted in each post office whereas it may be the case that all the letters are posted in a single post office. Similarly, if we proceed like that each post office can have six letters so number of ways is 6*6*6*6 = 6^4, there is also a fallacy, one letter cannot be posted in two post offices.)
I explained it because I had similar doubts about way of solving such problems so I thought you also might have.