In a playlist of 300 songs, 8 are from a specific group. The playlist is shuffled and played untilthe rth song from this group appears. Let Y denote the number of the songs from any other group that is played before the rth song from this group starts playing.

(a) Let r= 2. Find the probability the second song from this group appears on or after the20th song played.

(b) Let r= 3. Find the probability the fourth song from this group appears on or after the40th song played.

(c) Let r= 4. Find the expected number of songs from any other group that will be played before the fourth song from this group starts playing.

(d) Let r= 4. Find the variance of the number of songs from any other group that will be played before the fourth song from this group starts playing.