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,
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
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