Question

There are eleven songs on your playlist. five of them are country and six are pop. with random shuffle and no repetition, you listen to five songs. what is the probability that you listened to all country songs?

Answer 1

The probability is 1/462.

To find this, we will find the number of combinations of 5 country songs taken 5 at a time, 6 pop songs taken 0 at a time, and the total number of outcomes will be 11 songs taken 5 at a time:

$\frac{_5C_5\times_6C_0}{_{11}C_5} \\ \\\frac{\frac{5!}{5!0!}\times\frac{6!}{0!6!}}{\frac{11!}{5!6!}}=\frac{1\times1}{\frac{11!}{5!6!}} \\ \\=\frac{1}{462}$