A child received a gift of six different soccer team flags, including Liverpool and Arsenal. If he only has space in his bedroom to display four flags in a row, how many arrangements are possible if he cannot display the Liverpool and Arsenal flags at the same time?  Choose the correct choice from the following answers.
A) 162
B) 216
C) 272
D) 360
E) 414
The total number of ways to choose and arrange 4 flags out of 6 is C^46∗4!=360(or directly P^46).   We cannot have Liverpool and Arsenal flags at the same time. The number of ways to have and arrange Liverpool and Arsenal flags at the same time is C24∗4!=144 (choosing 2 flags out of 4 remaining, without Liverpool and Arsenal, and then arranging 4 flags with 4!);   Total - Restriction = 360 - 144= 
<gadget id="calculator">360 - 144</gadget>
<output>216</output>
216.   Answer: 216.
<result>B</result>
A child received a gift of six different soccer team flags, including Liverpool and Arsenal. If he only has space in his bedroom to display four flags in a row, how many arrangements are possible if he cannot display the Liverpool and Arsenal flags at the same time?