I assume, the order matters here.
[tex]k [/tex] objects can be chosen out of [tex] n [/tex] objects, when the order matters, in [tex] P(n,k)=\dfrac{n!}{(n-k)!} [/tex] ways.
So, the answer is [tex] P(8,4)=\dfrac{8!}{4!}=5\cdot6\cdot7\cdot8=1,680 [/tex] ways.
The number of ways the DJ can play 4 songs from 8 songs in the assembly is 70.
A permutation is an act of arranging the objects or elements in order. Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.
4 songs will be played during assembly but 8 songs were submitted.
The DJ choose 4 songs to play.
n = 8
r = 4
The number of ways the DJ can choose 4 songs from 8 will be
[tex]\rm Number \ of \ ways = \ ^nC_r \\\\Number \ of \ ways = \ ^8C_4\\\\Number \ of \ ways = \dfrac{8!}{(8-4)! * 4!}\\\\Number \ of \ ways = \dfrac{8!}{4! * 4!}\\\\Number \ of \ ways = \dfrac{8*7*6*5*4!}{4*3*2*1 * 4!}\\\\ Number \ of \ ways = 2*7*5\\\\Number \ of \ ways = 70[/tex]
The number of ways the DJ can choose 4 songs from 8 songs is 70.
More about the permutation and the combination link is given below.
https://brainly.com/question/11732255
