[Math] In how many ways can two oranges, one apple, and one banana be distributed to two distinguishable bags

Question

I have $2$ oranges, $1$ apple and $1$ banana. I want to put $2$ of them at a time in $2$ bags, having $1$ ($1$ fruit at max in $1$ bag) each.

The $2$ oranges are indistinguishable (there are two but their value is same).
[order does matter for combination]

The bags have positions: like first bag will be at first position and second will be at second position, and it will not be changed.

So please tell me in how many ways I can put them in bags?

yours sincerely

Answer 1

Let O be an orange, A be an apple, B be a banana.

There are 3 ways to put fruit in a bag with an orange in the first bag: OO OA OB

There are 2 ways to put fruit in a bag with an apple in the first bag: AO AB

There are 2 ways to put fruit in a bag with a banana in the first bag: BO BA

There has to be either an orange, apple, or banana put in the first bag so these are all 7 ways to put fruit into the two bags.