How to find the mean and variance of new combinations of old population?

I'm a late learner of maths &science.

Any books discuss these kind of problems?

3 groups of data:

f g h are their frequencies.

mean:

variance:

Find the mean and variance of

T can be many different operations.

for example:

T may be:

T may be:

T may be:

T may be:

T may be: , mean of two elements drawn from with replacement i=j is allowed.

T may be: , two elements drawn from without replacement where .

T may be: [????I don't know how it looks like.] is

T may be: , three elements drawn from without replacement where .

T may be: , a b c elements drawn from respectively with replacement.

T may be: [????I don't know how it looks like.], a b c elements drawn from respectively without replacement. I can't figure out the combination]