Question

A Dallas-area radio station plays songs from a specific, fixed set of artists. The station has no DJ; instead, a computer randomly selects which songs to play. The songs themselves are picked randomly, and the same song may be played many times in a row. In the set of songs, 45% are sung by a female singer, 40% are sung by a male singer, and 15% are instrumental with no vocals. What is the probability that a particular set of three songs contains one male singer, one female singer, and one instrumental? (Hint: Be aware that there are multiple ways to achieve this pattern of songs.)