Suppose you just purchased a digital music player and have put 15 tracks on it. After listening to them you decide that you like 3 of the songs. With the random feature on your player, each of the 15 songs is played once in random order. Find the probability that among the first two songs played you will like both of them

Question

Choi

Mathematics

31 May, 02:50

Suppose you just purchased a digital music player and have put 15 tracks on it. After listening to them you decide that you like 3 of the songs. With the random feature on your player, each of the 15 songs is played once in random order. Find the probability that among the first two songs played you will like both of them

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Francis Pollard · Answer 1

The given case is an example of permutation problem because the order is important given that you should like the first two songs. The sample space is calculated through the equation,

15P2 = 210

Then, there are 3 songs that you liked, the probability of picking 2 out of them is,

3P2 = 6

Dividing the latter by the earlier result will give us an answer of 1/35.