1. ## Permutation and combination

Question:

You put a CD that has 8 songs in your CD player.You set the player to play the songs at random.The player plays all 8 songs without repetition and you have 4 favourite songs on the CD.What is the outcome that 2 of your favourite songs are played first , in any order?

Thank you

2. Hello mj.alawami
Originally Posted by mj.alawami
Question:

You put a CD that has 8 songs in your CD player.You set the player to play the songs at random.The player plays all 8 songs without repetition and you have 4 favourite songs on the CD.What is the outcome that 2 of your favourite songs are played first , in any order?

Thank you
The number of arrangements of all $\displaystyle 8$ songs is $\displaystyle 8!$. The number of ways of choosing $\displaystyle 2$ favourites from $\displaystyle 4$ is $\displaystyle {^4C_2}$; the number of ways of arranging the remaining $\displaystyle 6$ songs is $\displaystyle 6!$.

So the probability is $\displaystyle \frac{{^4C_2}\times 6!}{8!}=\frac{3}{28}$

The probability that one of the 4 favourite songs is played first is $\displaystyle \frac{4}{8}$
and the probability that one of the remaining 3 favourites is played next is $\displaystyle \frac{3}{7}$
The probability of the first 2 songs being favourites is $\displaystyle \frac{4}{8}\ \frac{3}{7}$