From 3 apples, 4 plums and 2 grapefruits how many selections

Think of it this way:

How many ways you can choose from 3 apples?

2^3=8

atleast one apple has to be selected, which means (2^3-1). Similarly apply for other.

Thanks
Shishir

The notion 2^n is for the Yes/No answer. For each of the three apples, there are two choices: You can choose it (Y) or not choose it (N). So the total outcome for three apples would be 2^3. Now, since you have to choose at least one apple, this means you have to take out the one outcome where no apple is chosen (NNN). Therefore you get 2^3-1. Do the same thing for other fruits.

When the number of fruits for each type is not too big, baner's approach may be more straight forward.

How r we doing this without knowing the total number of selections to be made....im confused

The question itself is to find the total number of selections.

One of the selection with minimum number of fruits could be to select one from each category. Thus minimum fruits that can be choosen are 3 and maximum fruits that can be chosen are 9. So the number of fruits that can be choosen start from 3 upto 9. For each number the question need to know, how many ways can this selection be made. Example, 3 fruits can only be choosen in one way i.e 1 apple, 1 plum and 1 grapefruit. Similarly 4 fruits can be choosen in many ways

2 apples, 1 plums and 1 grapefruits
1 apples, 2 plums and 1 grapefruits
1 apples, 1 plums and 2 grapefruits

And so on.....

Hope I have not confused you further...

Ketan

ok now it makes sense
thanks mate!

HongHu:

Thanks !!! Thats it I could now get the concept.

Baner : your process of evaluation is right as always but I didnt know why this 2^n concept is being used.......

Bionomial Theorem says

nC0 + nC1 + nC2 +...nCn = 2^n

So the total # of combinations of 'n' things (taken in portions/all) = 2^n

this makes my concept clear..thanks honghu.