Question

There are fourteen songs on your playlist. Eight of them are country and six are

pop. With random shuffle and no repetition, you listen to eight songs. What is the
probability that you listened to exactly four country songs?
34.965%
40.793%
45.455%
18.357%

Answer 1

Answer: 34.965%

Explanation:

Number of ways of selecting 8 songs from 14 songs = = 14! / [ 8! × (14-8)! ]

= 14! / (8! × 6!)

= 3003

If you listended to exactly four country songs, then you should listen to four pop songs because you listened to 8 songs

Number of ways of selecting 4 country songs from total 8 country songs

= 8! / [ 4! × (8-4)! ]

= 8! / (4! × 4!)

= 70

Number of ways of selecting 4 pop songs from total 6 pop songs

= 6! / [ 4! × (6-4)! ]

= 6! / (4! × 2!)

= 15

Number of ways of playing 4 country songs and 4 pop songs in total 8 songs = 70 × 15

= 1050

So Probability that you listened to exactly four country songs =1050/3003

= 0.34965

= 34.965%