Exercise 27 Page 790

To find the probability that the first 8 songs in played in Kenneth's playlist are country songs, we need to find divide the number of successes and divide it by the number of possible outcomes. Let's find the number of possible outcomes first!

Number of Possible Outcomes

Since the order of the songs does not matter, we will find the combinations of n objects given r at a time. C( n, r)=n!/( n- r)! r!The total number of possible outcomes are the combinations of 18 songs taken 8 at a time. Let's substitute these values into the formula and simplify!

There are 43 758 posible outcomes.

Number of Successes

We know that there are 8 country songs. Since the order of the songs does not matter, there is just a single combination that has all country songs. There is 1 success.

Finding the Probability

Finally, we can find the probability by dividing the number of successes by the number of possible outcomes. Let's do it! P = Number of successes/Number of possible outcomes ⇓ P = 1/43 758 Therefore, the probability that the first 8 songs are country songs is 143 758.