Rolling a die $n$ times, how do you calculate the expected value of the number of results that appear more than once?

Question

If I roll a fair die that has $6$ sides $n$ times, what is the expected value of the number of outcomes that appear more than once?

Answer 1

To put you on track:

For $k=1,2,3,4,5,6$ let $B_{k}$ take value $1$ if face $k$ appears more than once and let it take value $0$ otherwise.

Now observe that $B:=\sum_{k=1}^{6}B_{k}$ equals the number of faces that appear more than once.

Find its expectation by means of linearity of expectation.