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,

MS4L

MathSolverForLYFE Jan 15, 2021

#1**+3 **

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

MooMooooMooM Jan 15, 2021

#2**+3 **

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)!

7!

_________________ =

3! * 2! * 2!

5040

________ = 210 identifiable orders

24

CPhill Jan 15, 2021

#3**+1 **

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