Suppose a compact disk (cd) you just purchased has 16tracks. after listening to the cd, you decide that you like 6of the songs. the random feature on your cd player will play each of the 16songs once in a random order. find the probability that among the first 5songs played (a) you like 2 of them; (b) you like 3 of them; (c) you like all 5of them.

(a) you like 2 of them
(6/16) × (5/15) × (10/14) × (9/13) × (8/12) = 21,600/524,160
(out of 524,160 total possible combinations for the first 5 songs, 21,600 combinations play 2 of the 6 liked songs)
simplified, 21,600/ 524,160 = 135/3,276
(this is about a 4% chance)

(b) you like 3 of them
(6/16) × (5/15) × (4/14) × (10/13) × (9/12) = 10,800/524,160
(out of 524,160 total possible combinations for the first 5 songs, 10,800 combinations play 3 of the 6 liked songs)
simplified, 10,800/524,160 = 135/6,552
(this is about a 2% chance)

(c) you like all 5 of them
(6/16) × (5/15) × (4/14) × (3/13) × (2/12) = 720/524,160
(out of 524,160 total possible combinations for the first 5 songs, only 720 combinations play 5 of the 6 liked songs)
simplified, 720/524,160 = 9/6,552
(this is about a 0.1% chance)