Mathematics: Permutation and combination 4 songs will be played during assembly but 8 songs were submitted. how many ways can the dj choose 4 songs to play? if you can, show your work and why you did what. you

Permutation and combination 4 songs will be played

Ответ:

reaganpodleski2

14.03.2022

The number of ways the DJ can play 4 songs from 8 songs in the assembly is 70.

What are permutation and combination?

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

$\rm Number \ of \ ways = \ ^nC_r \\\\Number \ of \ ways = \ ^8C_4\\\\Number \ of \ ways = \dfrac{8!}{(8-4)! * 4!}\\\\Number \ of \ ways = \dfrac{8!}{4! * 4!}\\\\Number \ of \ ways = \dfrac{8*7*6*5*4!}{4*3*2*1 * 4!}\\\\ Number \ of \ ways = 2*7*5\\\\Number \ of \ ways = 70$