Using the combination formula, it is found that there are 3300 ways to choose the songs.
The order in which the musics are chosen is not important, hence the combination formula is used to solve this question.
What is the combination formula?
��,�Cn,x is the number of different combinations of x objects from a set of n elements, given by:
��,�=�!�!(�−�)!Cn,x=x!(n−x)!n!
For the rock songs, we have three from a set of eleven, hence:
�11,3=11!3!8!=165C11,3=3!8!11!=165
For the alternative songs, we have four from a set of five, hence:
�5,4=5!4!1!=5C5,4=4!1!5!=5
For the rap songs, we have three from a set of four, hence:
�4,3=4!3!1!=4C4,3=3!1!4!=4
Since the songs are independent, the total number of ways is given by:
�=165×5×4=3300T=165×5×4=3300
hope this helps you