CAN YOU USE THE INDICATOR METHOD, AND CAREFULLY EXPLAIN HOW YOU GET EACH PROBABILITY THANKS

I roll a fair die four times. Let X be the number of different outcomes that I see. (For example, if the die rolls are 5, 3, 6, 6 then X = 3 because the different outcomes are 3, 5 and 6.)

(a) Find the mean of X.

(b) Find the variance of X.