# Math Help - Permutation and combination

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

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

3. Alternatively,

The probability that one of the 4 favourite songs is played first is $\frac{4}{8}$

and the probability that one of the remaining 3 favourites is played next is $\frac{3}{7}$
because the songs are played without repetition.

The probability of the first 2 songs being favourites is $\frac{4}{8}\ \frac{3}{7}$

This includes the probability of F1 being played before F2 and F2 being played before F1 (all possible arrangements), hence if the order does not matter, dividing by 2! (to unarrange the songs) will give the probability of the first 2 songs being favourites irrespective of order.