How to select at least one mango and one orange? A bag contains $4$ mangoes and $5$ oranges. In how many ways can I make a selection so as to take at least one mango and one orange?
In my book it is given $(2^4-1)(2^5-1)$
I understood $1$ is subtracted because if no mango is chosen. But why is it $2^4$ and $2^5$?
Please help.

I guess that a selection here means a non-empty subset of fruits.
Now there are $2^9-1$ possible non-empty subsets out of a bag of $9$ fruits, $2^4-1$ contain only mangoes and $2^5-1$ contain only oranges.
What may we conclude?
P.S. Recall that if $S$ is a finite set with $n$ elements, then the number of subsets of $S$ is $2^n$ (see the wiki page Power set)
