Question

To choose the 8 songs, the director writes the name of each of the 12 songs on a slip of paper, puts them in a hat, and draws 8 slips. What is the probability that the set s/he chooses contains two of the four songs that have soprano solos?

Answer 1

0.339

Explanation:

Given that :

Total number of songs = 12

Number of songs to choose = 8

Total number of draws = 8

Selecting 2 of the 4 songs with syprano solos : 4C2

The 6 remaining songs from. The rest:

12-4C8-2 = 8C6

Total possible selections = 12C8

Hence,

probability that the set s/he chooses contains two of the four songs that have soprano solos will be :

(4C2 * 8C6) / 12C8

(6 * 28) / 495

168 / 495

= 0.339