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

34.965%

Explanation:

What we must do is calculate the number of possible combinations there are and divide by the total number of combinations,

For country music, there are 8 of them, but we want 4 to sound, therefore it is 4 taken from 8, that is to say 8C4

and there are still 4 songs to listen to, which must be pop, there are 6 songs from pop, therefore it is 4 taken from 6, that is to say 6C4

The total number of combinations would be all the songs and that 8 of them are chosen, that is, 14C8

So it would be: 8C4 * 6C4 / 14C8

nCr = n! / r! (n-r)!

replacing each one:

8C4 = 8! / (4! * 4!) = 70

6C4 = 6! / (4! * 2!) = 15

14C8 = 14! / (8! * 6!) = 3003

replacing:

70 * 15/3003 = 0.34965

In other words, the probability is 34.965%

Answer 2

Answer: 34.965%

Explanation:

No. 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%