compact disk that will have 5 songs

Question

How many ways can I arrange the 5 songs on the cd?

Answer 1

 

first song you are choosing from 5 songs

second song you are choosing from 4 songs

third, choose from 3

fourth, choose from 2

fifth, choose from 1

5*4*3*2*1=120 ways

suppose you have 3 songs, A, B, C

3*2*1=6 ways

ABC

ACB

BAC

BCA

CAB

CBA

if you had 4 songs, 4*3*2*1=24 ways

A, B, C, D

ABCD, ABDC, ADBC, DABC

ACBD, ACDB, ADCB, DACB

4 more ways for BAC

4 more ways for BCA

4 more ways for CAB

4 more ways for CBA

24 ways

if you had 1 more song (5 songs), there would be 5 ways to position the 5th song E for each of the 4-song permutations

for example:

ABCDE, ABCED, ABECD, AEBCD, EABCD

there are 24 permutations times 5 positions for each giving you 120 ways (permutations)