Solutions to Practice Problems for  the Lander Math Contest
Module 5, Solutions (13-15):

13) The number of possibilities to place two heads in five
spots is 5x4/2=10. The total number of outcomes in five
tosses is 2^5=36. Then, the probability of getting exactly two
heads in five tosses is equal to 10/36=5/18.

14) The number of possibilities to place three heads in six
spots is (6x5x4)/(2x3)=20. The total number of outcomes in
five tosses is 2^6=64. Then, the probability of getting exactly
three heads in six tosses is equal to 20/64=5/18.

15) The probability of getting exactly three heads in five
tosses (three heads and two tails) is the same as the
probability of getting exactly two heads in five tosses (three
tails and two heads) – 5/18.