Suppose Tina is throwing a surprise party to celebrate her friend Trevor's birthday, and she asks her good friend Tom to help with the music. The two agree to create a joint song playlist for Trevor to listen to during the car ride to the party. Tina chooses to add six songs to the playlist, and Tom chooses to add nine songs. Suppose the playlist they created is significantly too long, and the car ride will only last long enough for the three to hear five of the songs on the playlist. Also, suppose that each time a song is selected to be played, it is randomly selected from the remaining songs withoutreplacement.

After careful consideration, Tina is a little worried about Tom's song choices and hopes that Trevor will not hear too many of his songs. Let?

be the random variable representing the number of Tom's songs that are played during the car ride. Calculate the probability that Trevor will hear zero, one, or two of Tom's song choices. Round your answers to the nearest three decimalplaces.

?(?=0)=

?(?=1)=

?(?=2)=

Finally, calculate the probability that at most two of Tom's song choices are played during the car ride. Please round your answer to the nearest three decimalplaces.

?(?2)=