How to select at least one mango and one orange?

Question

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.

To "make a selection" means to select how many out of the bag? — Jimmy R., Dec 06 '16 at 10:11
Instead of repeating your call for help, you should answer @JimmyR.'s question: how many pieces of fruit are you supposed to take? Or even better: provide sufficient context in your question. — StackTD, Dec 06 '16 at 10:15

score 1 · Answer 1 · answered Dec 06 '16 at 10:19

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)

1 Answers1