Answer
a) 1024
b) 45
c) 176
d) 252
Work Step by Step
a) Since each flip can be either be a heads or tails, so there are $2^{10}$ = 1024 possible outcomes.
b) We need to find the possible number of cases when we have exactly two heads, for this we simply need to choose the two flips that came up
heads. There are $^{10}C_2$ = 45 such outcomes.
c) Since we need at most three tails, which means we can have three tails, two tails, one tail, or no tails.
As we did in part (b), we see that there are
$$^{10}C_3+^{10}C_2+^{10}C_1+^{10}C_0 = 120 + 45 + 10 + 1 = 176 $$
such outcomes.
d) To contain equal number of heads and tails in this case means to have five heads and five tails.
Therefore the answer $^{10}C_5 = 252$.
