I love eating fresh fruits. I recently started a order chart on different fruits I can eat throughout a week. Since, I love bananas, I chose to have $3$ bananas every week. Kiwis aren't bad, I'll do $2$ each week. Same with the humble apple, $2$ will suffice! And, of course, I want them to be indistinguishable because an apple, is an apple (unless its gone bad)! I was wondering how many different orders I could eat these fruits? Here's an example:

BBBKKAA (Banana, Banana, Banana, Kiwi, Kiwi, Apple, Apple)

Please help me with this so I can try to mix up my order every week to have some more variety than just eating in the BBBKKAA order. Also, I would like it if you explain so I can do this myself.


Thanks in advance,







 Jan 15, 2021

There are 7! ways to order 7 objects but there are repeats

Divide 7! by 3! because there are 3  bananas and you can order 3 items 3! ways

Do the same with the other two fruits

 Jan 15, 2021

This is equivalent to the  number  of  distinguishable  "words" we can make from  BBBKKAA   =


                    (Number  of Letters ) !


(Number of Bs)! * ( Number of Ks)! * (Number of As)!




                _________________  =

                   3!   *   2!    *   2!




                      ________  =           210  identifiable orders




cool cool cool

 Jan 15, 2021

Thank you Chris! I expected it to be something with permutations! Much thanks to the reply above, MooMooooMooM! I have to go for the night, have a great day/night/morning/noon/evening wherever you are!

MathSolverForLYFE  Jan 15, 2021

88 Online Users