Question

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

Answer 1

Answer: 34.965%

Step-by-step 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%

Answer 2

Answer:

34.965%

Step-by-step 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%