Exact number of events to get the expected outcoms Suppose in a competition 11 matches are to be played, each having one of 3
distinct outcomes as possibilities. How many number of ways one can predict the
outcomes of all 11 matches such that exactly 6 of the predictions turn out to
be correct?

The  $6$ matches on which our prediction is correct can be chosen in $\binom{11}{6}$ ways. For each of these choices, we can make wrong predictions on the remaining $5$ matches in $2^5$ ways. Thus the total number is
$$\binom{11}{6}2^5.$$
